Sample of 152 SAMPLE OF 152 Basic parameters of observed anthropometric characteristics

Sample of 152

SAMPLE OF 152

Basic parameters of observed anthropometric characteristics and dimensions of the liver referring to the entire sample

Central and dispersion parameters, measures of asymmetry and flatness for anthropometric characteristics and liver dimensions represent the entire sample. On the basis of this parameters, we will determine if conditions are met for application of the parametric tests.

Table 4 Central and dispersion parameters, measures of asymmetry and flatness for anthropometric characteristics and dimensions of the liver for the entire sample (152)

mean

error

min

max

hgt

170.84

10.35

.84

117.0

197.0

6.06

169.18

172.50

-.73

3.77

.066

wgt

74.69

12.81

1.04

50.0

120.0

17.15

72.64

76.74

.89

1.26

.001

BMI

25.65

4.40

.36

17.3

57.0

17.14

24.94

26.35

2.70

15.78

.000

D-il

20.40

2.93

.24

13.2

30.8

14.39

19.93

20.87

.36

.62

.086

ApBo

23.84

3.88

.31

16.2

35.8

16.27

23.22

24.47

.57

.49

.100

TvBo

33.22

3.73

.30

25.1

46.7

11.24

32.62

33.81

.64

.89

.056

MxAp

16.98

2.35

.19

12.3

24.0

13.85

16.60

17.35

.25

-.25

.021

MxCo

18.24

2.59

.21

13.4

26.8

14.17

17.83

18.66

.72

.44

.007

MxCr

16.53

2.32

.19

11.6

25.1

14.02

16.16

16.90

.48

.68

.108

MxCc

16.85

2.20

.18

12.0

24.4

13.03

16.50

17.20

.58

.63

.058

Comx

19.05

2.67

.22

14.9

26.8

14.02

18.62

19.48

.63

-.14

.019

Vcal

1589.54

412.09

33.42

879.3

3385.5

25.92

1523.48

1655.59

1.22

2.61

.001

VCt

1550.71

367.74

29.83

853.2

3092.3

23.71

1491.76

1609.66

1.22

2.74

.000

A note: The values for asymmetry and kurtosis between -.04 and .04 were not discussed

Minimal (min) and Maximal (max) values of anthropometric and linear hepatic measurements for 152 examinees fall well within the expected range of values. Higher values of the coefficient of variation show heterogenity of the sample for liver volume (calculated by formula) (Vcal) (25.92), CT Liver volumetry (VCt) (23.71). The values of coefficient of variation (CV) show homogenity for: height (hgt) (6.06), weight (wgt) (17.15), BMI (BMI) (17.14), Diaphragm to iliac (D-il) (14.39), AP body dimension (ApBo) (16.27), Transverse body dimension (TvBo) (11.24), Maximal Ap (MxAp) (13.85), Maximal Coronal (MxCo) (14.17), Maximal Crainocaudal (MxCr) (14.02), Max CC (MxCc) (13.03), Cormax LL (Comx) (14.02). Increased values of Skewness (sk) show that distribution is negatively asymmetrical or Negatively Skewed Curve, This represents a frequency distribution in which comparatively more scores fall in higher classes, it has higher values than in the normal distribution for: weight (wgt) (.89), BMI (BMI) (2.70), Diaphragm to iliac (D-il) (.36), AP body dimension (ApBo) (.57), Transverse body dimension (TvBo) (.64), Maximal Ap (MxAp) (.25), Maximal Coronal (MxCo) (.72), Maximal Crainocaudal (MxCr) (.48), Max CC (MxCc) (.58), Cormax LL (Comx) (.63), liver volume (calculated by formula) (Vcal) (1.22), CT Liver volumetry (VCt) (1.22). Decreased values of Skewness (sk) show that distribution is positively asymmetrical or Positively Skewed Curve. Such a curve results from a frequency distribution where observation concentrate in lower classes, it has more lower values compared to normal distribution, for: height (hgt) (-.73). The higher values of Kurtosis (ku) indicate that curve is elongated for: height (hgt) (3.77), weight (wgt) (1.26), BMI (BMI) (15.78), Diaphragm to iliac (D-il) (.62), AP body dimension (ApBo) (.49), Transverse body dimension (TvBo) (.89), Maximal Coronal (MxCo) (.44), Maximal Crainocaudal (MxCr) (.68), Max CC (MxCc) (.63), liver volume (calculated by formula) (Vcal) (2.61), CT Liver volumetry (VCt) (2.74). A negative kurtosis (k) means that distribution is flatter than a normal curve for: Maximal Ap (MxAp) (-.25), Cormax LL (Comx) (-.14). Distribution (p) is approximately normal for: AP body dimension (ApBo) (.10), Maximal Crainocaudal (MxCr) (.11). The data does not follow a normal distribution (p) for: height (hgt) (.07), weight (wgt) (.00), BMI (BMI) (.00), Diaphragm to iliac (D-il) (.09), Transverse body dimension (TvBo) (.06), Maximal Ap (MxAp) (.02), Maximal Coronal (MxCo) (.01), Max CC (MxCc) (.06), Cormax LL (Comx) (.02), liver volume (calculated by formula) (Vcal) (.00), CT Liver volumetry (VCt) (.00).

Alalysis of anthropometric and linear hepatic measurements

According to the specific research purpose for the structure of anthropometric and linear hepatic measurements, from the sample of 152 examinees, we have chosen optimal number of factors, using method of Factor analysis of the main components, on the basis of 10 anthropometric and linear hepatic measurements: height (hgt), weight (wgt), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx). The aim of Factor analysis is to determine the relationships among the set of observed variables, to determine the contribution of a factor to each variable, contribution of each variable to a factor, to apply complementary analyses and to present the results Graphically. We will present the coordinates of each anthropometric and linear hepatic measurement to determine their position in isolated structure.

In the table “Structure of isolated factors” columns are: inr -Inertia; F-factor coordinate; cor- contribution of each factor to a variable; ctr- contribution of each variable to a factor. The results given in the tables are multiplied by 1000.

Structure of 4 isolated factors for anthropometric and linear hepatic measurements

In this chapter we analysed the structure of four isolated factors (Principal Component Analysis) from 10 anthropometric and linear hepatic measurements: height (hgt), weight (wgt), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx). The sample consisted of 152 examinees.

Table 1 The correlation matrix

hgt

Wgt

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

hgt

1000

wgt

508

1000

D-il

422

1000

ApBo

594

332

1000

TvBo

654

400

813

1000

MxAp

251

528

264

637

485

1000

MxCo

121

-37

-22

-135

1000

MxCr

207

147

299

169

111

142

1000

MxCc

248

307

384

319

265

233

168

906

1000

Comx

230

176

204

784

140

200

1000

We found the strongest correlations (906) between Max CC (MxCc) and Maximal Crainocaudal (MxCr). The strongest negative correlation is -135 between Maximal Coronal (MxCo) and Maximal Ap (MxAp).

Table 2 The characteristic square of a factor and the percentage contribution

square

sum

3.619

36.193

2.030

20.300

56.493

1.442

14.423

70.916

1.077

10.773

81.689

.707

7.068

88.757

.517

5.170

93.927

.206

2.063

95.990

.191

1.910

97.900

.140

1.395

99.295

.070

.705

100.000

Percentage representation of the characteristic squares fall in the range between .705% and 36.193%. The new structure is formed of 4 isolated factors which contain 81.689 % information from the whole sample.

Table 3 Structure of four isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

4 -factor

qlt

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

941

-408

167

228

-119

842

709

658

wgt

816

-806

650

180

-181

-228

286

D-il

450

-608

370

102

-263

ApBo

847

-779

607

168

-391

153

-105

-277

TvBo

815

-767

588

163

-366

134

-174

-251

MxAp

624

-661

437

121

-388

150

-132

139

MxCo

892

-156

774

599

295

-474

225

156

-207

MxCr

949

-499

249

480

230

113

686

470

326

-19

MxCc

941

-659

435

120

412

170

579

335

233

-30

Comx

893

-307

710

504

248

-530

281

195

-120

1000

The factor structure for anthropometric and linear hepatic measurements

Factor analysis reduced the set of data (10 anthropometric and linear hepatic measurements) to 4 isolated factors. The contribution of isolated factors (qlt) is significant for 10 anthropometric and linear hepatic measurements.

* The communality is higher for: Maximal Crainocaudal (MxCr) 949, height (hgt) 941, Max CC (MxCc) 941, Cormax LL (Comx) 893, Maximal Coronal (MxCo) 892, AP body dimension (ApBo) 847, weight (wgt) 816, Transverse body dimension (TvBo) 815, Maximal Ap (MxAp) 624.

* Intermediate communality shows that the structure of 4 isolated factors contain intermediate amount of information about anthropometric and linear hepatic measurements: Diaphragm to iliac (D-il) 450.

The variables that contribute in forming the structure of each isolated factor are: Maximal Crainocaudal, height, Max CC, Cormax LL, Maximal Coronal, AP body dimension, weight, Transverse body dimension, Maximal Ap, Diaphragm to iliac, the variables that do not contribute to factor structure are:

* Structure of the 1st- isolated factor is formed of 5 anthropometric and linear hepatic measurements: weight (wgt) with factor contribution (cor) 650, AP body dimension (ApBo) 607, Transverse body dimension (TvBo) 589, Maximal Ap (MxAp) 437, Max CC (MxCc) 435. Latent variable is: Diaphragm to iliac (D-il) 370. Weighting is in concordance with: AP body dimension, Transverse body dimension, Maximal Ap, Max CC, Diaphragm to iliac.

* Structure of the 2nd- isolated factor is formed of 2 anthropometric and linear hepatic measurements: Maximal Coronal (MxCo) with factor contribution (cor) 600, Cormax LL (Comx) 505. Association Weighting Maximal Coronal is in concordance with: Cormax LL.

* Structure of the 3rd- isolated factor is formed of 1 anthropometric and linear hepatic measurement : Maximal Crainocaudal (MxCr) with factor contribution (cor) of 470. Latent variables are: Max CC (MxCc) 336, Cormax LL (Comx) 281. Association of Maximal Crainocaudal is in concordance with: Max CC. Association of Maximal Crainocaudal is inversely proportional with: Cormax LL.

* Structure 4.- isolated factor is formed of 1 anthropometric and linear hepatic measurement : height (hgt) with factor contribution (cor) 709.

* Several factors contribute to variable for: Max CC, factor-1 (435), factor-3 (336), Cormax LL, factor-2 (505), factor-3 (281).

In forming the structure of two and more factors contribute 2 anthropometric and linear hepatic measurements. All 10 (100.00%) anthropometric and linear hepatic measurements contribute in forming the structure of isolated factors.

Concordance of anthropometric and linear hepatic measurements and Structure of isolated factors

In forming the structure of 4 isolated factors from the sample of 152 examinees 131 (86.18%) examinees have high contribution, 14 (9.21%) examinees have intermediate contribution, 7 (4.61%) examinees have low contribution without significance .

1. – The anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor for 46 examinees (30.26%). Latently related to the structure are 19 examinees (12.50%). For 29 examinees we found direct proportionality, and 36 were inversely related.

2. – The anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor for 31 examinees (20.39%). Latently related to the structure for 21 (13.82%) examinees. For 24 examinees we found direct proportionality, and 28 were inversely related.

3. – The anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor for 19 examinees (12.50%). Latently related to the structure for 18 (11.84%) examinees. For 15 examinees we found direct proportionality, and 22 were inversely related.

4. – The anthropometric and linear hepatic measurements are highly concordant with the structure 4 isolated factor for 11 examinees (7.24%). Latently related to the structure for 12 (7.89%) examinees. For 11 we found direct proportionality, and 12 were inversely related.

Accordance of anthropometric and linear hepatic measurements with the structure: two and more factor have 3 examinees , one factor have 101 examinees, latent agreement only have 37 examinees , with no agreement are 11 .

It should be noted that 2 examinees stand out from the rest (inr)

Graph 1 Graphicalal representation of anthropometric and linear hepatic measurements in each isolated factor structure

Graph 2 Graphical representation of anthropometric and linear hepatic measurements in isolated factor structures 1F and 2F

Graph 3 Graphicalal representation of anthropometric and linear hepatic measurements in isolated factor structures 1F and 3F

Graph 4 Graphical representation of anthropometric and linear hepatic measurements in isolated factor structures 2F and 3F

Structure of 4 isolated factors for anthropometric and linear hepatic measurements

In this chapter we analysed the structure of 4 isolated factors (Principal Component Analysis) from 13 anthropometric and linear hepatic measurements: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal), CT Liver volumetry (VCt). The sample consisted of 152 examinees.

Table 5 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

508

1000

BMI

-326

621

1000

D-il

422

387

1000

ApBo

594

608

332

1000

TvBo

654

615

400

813

1000

MxAp

251

528

385

264

637

485

1000

MxCo

121

-66

-37

-22

-135

1000

MxCr

207

147

-24

299

169

111

142

1000

MxCc

248

307

116

384

319

265

233

168

906

1000

Comx

230

176

204

784

140

200

1000

Vcal

328

424

186

369

457

346

531

533

692

750

514

1000

VCt

280

446

255

386

502

372

566

403

651

729

446

928

We found the strongest correlations (928) between CT Liver volumetry (VCt) and liver volume (calculated by formula) (Vcal), the strongest negative correlation is -326 between BMI (BMI) and height (hgt).

Table 6 The characteristic square of a factor and the percentage contribution

sqare

sum

5.268

40.523

2.585

19.882

60.405

1.483

11.404

71.809

1.256

9.661

81.470

.841

6.468

87.938

.583

4.488

92.426

.433

3.331

95.757

.211

1.626

97.383

.142

1.095

98.478

.098

.751

99.229

.075

.574

99.804

.019

.148

99.952

.006

.048

100.000

Percentage representation of the characteristic squares fall in the range between .048% to 40.523%. The new structure is consisted of 4 isolated factors which contain 81.470 % information from the whole sample.

Table 7 Structure of 4 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

4 -factor

qlt

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

943

343

118

280

-45

863

745

593

wgt

811

721

520

-373

139

146

362

131

104

BMI

843

490

240

-646

417

161

211

-377

142

113

D-il

377

569

324

-117

-3

-200

ApBo

785

717

514

-514

264

102

-61

TvBo

752

665

443

-541

292

113

126

-25

MxAp

641

640

410

-373

139

-29

300

MxCo

914

305

627

393

152

634

402

271

-161

MxCr

939

590

348

469

220

-572

327

221

-210

MxCc

920

729

531

101

356

127

-484

234

158

-168

Comx

878

410

168

529

280

108

655

429

289

-35

Vcal

925

882

779

148

381

145

-10

-37

VCt

864

884

781

148

276

-59

-54

1000

The factor structure for anthropometric and linear hepatic measurements

Whole sample that consisted of 13 anthropometric and linear hepatic measurements is reduced to 4 isolated factors. The contribution of isolated factors (qlt) is significant for 12 anthropometric and linear hepatic measurements.

* The communality is higher for: height (hgt) 943, Maximal Crainocaudal (MxCr) 939, liver volume (calculated by formula) (Vcal) 925, Max CC (MxCc) 920, Maximal Coronal (MxCo) 914, Cormax LL (Comx) 878, CT Liver volumetry (VCt) 864, BMI (BMI) 843, weight (wgt) 811, AP body dimension (ApBo) 785, Transverse body dimension (TvBo) 752, Maximal Ap (MxAp) 641.

* Decreased communality shows that the structure of 4 isolated factors does not contain enough information about: Diaphragm to iliac (D-il) 377

The variables that contribute in forming the structure of each isolated factor are: height, Maximal Crainocaudal, liver volume 01 (calculated by formula), Max CC, Maximal Coronal, Cormax LL, CT Liver volumetry, BMI, weight, AP body dimension, Transverse body dimension, Maximal Ap, the variable that do not contribute to factor structure is: Diaphragm to iliac.

* Structure of the 1st- isolated factor is formed of 7 anthropometric and linear hepatic measurements: CT Liver volumetry (VCt) with factor contribution (cor) 782, liver volume (calculated by formula) (Vcal) 779, Max CC (MxCc) 531, weight (wgt) 520, AP body dimension (ApBo) 515, Transverse body dimension (TvBo) 443, Maximal Ap (MxAp) 411. Latent variables are: Maximal Crainocaudal (MxCr) 349, Diaphragm to iliac (D-il) 324. Association of the CT Liver volumetry is in concordance with: liver volume (calculated by formula), Max CC, weight, AP body dimension, Transverse body dimension, Maximal Ap, Maximal Crainocaudal, Diaphragm to iliac.

* Structure of the 2nd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: BMI (BMI) with factor contribution (cor) 418. Latent variables are: Maximal Coronal (MxCo) 393, Transverse body dimension (TvBo) 293, Cormax LL (Comx) 280. Association of BMI is in concordance with: Transverse body dimension. Association of BMI is inversely proportional with: Maximal Coronal, Cormax LL.

* Structure of the 3rd- isolated factor is formed of 2 anthropometric and linear hepatic measurements: Cormax LL (Comx) with factor contribution (cor) 429, Maximal Coronal (MxCo) 403. Latent variables are: Maximal Crainocaudal (MxCr) 327. Association Cormax LL is in concordance with: Maximal Coronal. Association Cormax LL is inversely proportional with: Maximal Crainocaudal.

* Structure 4.- isolated factor is formed of 1 anthropometric and linear hepatic measurement: height (hgt) with factor contribution (cor) 746.

* Several factors contribute to variable for: Transverse body dimension, factor-1 (443), factor-2 (293), Maximal Coronal, factor-2 (393), factor-3 (403), Maximal Crainocaudal, factor-1 (349), factor-3 (327), Cormax LL, factor-2 (280), factor-3 (429).

All 13 (100.00%) anthropometric and linear hepatic measurements contribute in forming the structure of 4 anthropometric and linear hepatic measurements.

Concordance between anthropometric and linear hepatic measurements and Structure of isolated factors

In forming the structure of 4 isolated factors 126 (82.89%) examinees have high contribution, 15 (9.87%) examinees have intermediate contribution, 11 (7.24%) examinees have low contribution without significance.

1. – for 54 (35.53%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 15 (9.87%) examinees. For 29 examinees we found direct proportionality, and 40 were inversely related.

2. – for 30 (19.74%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure are 14 (9.21%) examinees. For 19 examinees we found direct proportionality, and 25 were inversely related.

3. – for 16 (10.53%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure are 13 (8.55%) examinees. For 13 examinees we found direct proportionality, and 16 examinees were inversely related.

4. – for 6 (3.95%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 4 isolated factor. Latently related to the structure are 12 (7.89%) examinees. For 11 we found direct proportionality, and 7 were inversely related.

Concordance anthropometric and linear hepatic measurements with the structure: two and more factor have 2 examinees, one factor have 102 examinees, latent agreement only have 32 examinees, with no agreement are 16 examinees.

It should be noted that 3 examinees stand out from the rest (inr)

Graph 5 Graphicalal representation of anthropometric and linear hepatic measurements in the isolated factors structures

Graph 6 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structures 1F and 2F

Graph 7 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factor structures 1F and 3F

Graph 8 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factor structures 2F and 3F

The mutual contribution of the division classes and factors structure anthropometric and linear hepatic measurements

Table 9 Contributions among gender groups (2) and structure of isolated factors for anthropometric and linear hepatic measurements

1-factor

2-factor

3-factor

4-factor

mass

inr

kvl

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

Sex-1

441

1000

808

637

-167

581

329

118

Sex-2

559

1000

-637

637

132

-64

-458

329

As shown in Table 9, the highest weight coefficient is 559 for the class Sex-2 which means that the largest part of the sample belonging to one class, is in that class to which the specified weighting coefficient corresponds, and the next is for the class Sex-1 (441.).

* Inertia (inr) is 35 for the class Sex-1, it means that this class the most stands out from the rest, and the next is for the class: Sex-2 (27.).

* Relative contribution (cor) 1. – of the axis to the class for Sex-1 is high 637, which means that the axis has the most information about that class, then for: Sex-2 (637-high). Relative contribution 2. – of the axis to the class for Sex-1 is 27- without significance, then for: Sex-2 (27-without significance). Relative contribution 3. – of the axis to the class for Sex-1 is 6 without significance, then for: Sex-2 (6-without significance). Relative contribution 4. – of the axis to the class for Sex-1 is 329, that is low, and then for: Sex-2 (329-also low).

* Relative contribution of the class Sex-1 to the inertia 1. – axis is 55i4r, then for: Sex-2 (43). Relative contribution of the class Sex-1 to the to inertia of the 2nd – axis is 5, then for: Sex-2 (4). Relative contribution of the class Sex-1 to inertia of the 3rd – axis is 2, then for: Sex-2 (2.). Relative contribution of the class Sex-1 inertia 4. – axis is 118, then for: Sex-2 (93).

Table 10 Contribution of a factor to a klasi in ‰:

Sex-1

637

329

Sex-2

637

329

* The highest contribution to the class Sex-1 gives factor F1 (637‰) then F2 (27‰) which contributess 23.6 times less, then F4 (329‰) which contributess 1.9 times less. The highest contribution to the class Sex-2 is factor F1 (637 ‰) then F2 (27‰) which contributess 23.6 times less, and then F4 (329‰) which contributess 1.9 times less.

for the 1st- axis (226) then for the 3rd- axis (2), the 4th- axis (117).

Table 13 Mahalanobis distance between the two gender groups for anthropometric and linear hepatic measurements

Sex-1

Sex-2

Sex-1

.00

1.38

Sex-2

1.38

.00

By calculating Mahalanobis distance between genders, we obtained another indicator of similarities or differences. Distances of different spaces can be compared.

According to the results in table 13 we can say that distance between gender groups Sex-1 and Sex-2 (Sex-1 and Sex-2) is bigger.

GENDER DIFFERENCES IN A SAMPLE OF 152 ADULTS

Gender analysis for anthropometric and linear hepatic measurements

In accordance to the previously established design of the study, we will analyse anthropometric and linear hepatic measurements in relation to gender.

The Central and dispersion parameters in relation to gender are presented both in tables and Graphically as well as measures of asymmetry and flatness. Gender differences will be analysed in the in the second part, ie hypotheses will be accepted or rejected, in order to assess the results and the usefulness of further analysis, determine the directions and methodological priorities. If the conditions are met, we will define the characteristics and homogeneity of each gender group, and determine the distance between them. The results will be presented Graphically.

We will analyse anthropometric and linear hepatic measurements: height, weight, BMI, Diaphragm to iliac, AP body dimension, Transverse body dimension, Maximal Ap, Maximal Coronal, Maximal Crainocaudal, Max CC, Cormax LL, liver volume (calculated by formula), CT Liver volumetry, The sample consisting of 152 examinees is divided into two gender groups: Sex-1 (67) and Sex-2 (85).

Descriptive statistics for gender groups

Central and dispersion parameters, measures of asymmetry and flatness for anthropometric and linear hepatic measurements are presented for each gender group and we are investigating the possibility of applying parametric procedures.

Table 14 Central and dispersion parameters and measures of asymmetry and flatness for anthropometric and linear hepatic measurements in the group Sex-1 (67)

mean

min

max

hgt

176.15

11.39

117.0

197.0

6.47

173.37

178.93

-2.23

9.61

.525

wgt

80.42

13.03

58.0

120.0

16.21

77.24

83.60

.91

1.00

.147

BMI

26.14

5.36

18.9

57.0

20.52

24.83

27.45

3.09

14.65

.007

D-il

20.61

3.25

13.3

30.8

15.78

19.82

21.41

.23

.923

ApBo

24.83

4.01

16.2

35.8

16.15

23.85

25.81

.68

.48

.488

TvBo

33.91

3.69

27.9

44.5

10.89

33.01

34.81

.63

.01

.627

MxAp

18.19

2.15

13.7

24.0

11.84

17.67

18.72

.18

.29

.810

MxCo

18.09

2.28

13.8

26.8

12.61

17.54

18.65

1.22

2.54

.116

MxCr

16.51

2.74

11.6

25.1

16.58

15.84

17.18

.60

.61

.855

MxCc

17.02

2.62

12.0

24.4

15.38

16.38

17.66

.60

.34

.882

Comx

19.46

2.46

15.5

26.8

12.66

18.86

20.07

.64

.17

.373

Vcal

1697.18

475.35

1051.2

3385.5

28.01

1581.21

1813.16

1.21

2.02

.441

VCt

1671.51

408.43

1118.2

3092.3

24.43

1571.86

1771.15

1.37

2.43

.304

A note: The values for asymmetry and flatness between -.04 and .04 are not discussed

According to Minimum (min) and Maximum (max) for anthropometric and linear hepatic measurements in the group Sex-1 we can say that values fall well within the expected range. The higher values of coefficient of variation (CV) mean that group Sex-1 is heterogeneous in: BMI (BMI) (20.52), liver volume (calculated by formula) (Vcal) (28.01), CT Liver volumetry (VCt) (24.43). According to coefficient of variation (CV) the group Sex-1 is homogenous fror variables: height (hgt) (6.47), weight (wgt) (16.21), Diaphragm to iliac (D-il) (15.78), AP body dimension (ApBo) (16.15), Transverse body dimension (TvBo) (10.89), Maximal Ap (MxAp) (11.84), Maximal Coronal (MxCo) (12.61), Maximal Crainocaudal (MxCr) (16.58), Max CC (MxCc) (15.38), Cormax LL (Comx) (12.66). Increased values of Skewness (sk) show that distribution is negatively asymmetrical or Negatively Skewed Curve, This represents a frequency distribution in which comparatively more scores fall in higher classes, it has higher values than in the normal distribution for: weight (wgt) (.91), BMI (BMI) (3.09), Diaphragm to iliac (D-il) (.23), AP body dimension (ApBo) (.68), Transverse body dimension (TvBo) (.63), Maximal Ap (MxAp) (.18), Maximal Coronal (MxCo) (1.22), Maximal Crainocaudal (MxCr) (.60), Max CC (MxCc) (.60), Cormax LL (Comx) (.64), liver volume (calculated by formula) (Vcal) (1.21), CT Liver volumetry (VCt) (1.37). Decreased values of Skewness (sk) show that distribution is positively asymmetrical or Positively Skewed Curve. Such a curve results from a frequency distribution where observation concentrate in lower classes, it has more lower values compared to normal distribution, for: height (hgt) (-2.23). The higher values of Kurtosis (k) indicate that curve is elongated for: height (hgt) (9.61), weight (wgt) (1.00), BMI (BMI) (14.65), Diaphragm to iliac (D-il) (.23), AP body dimension (ApBo) (.48), Maximal Ap (MxAp) (.29), Maximal Coronal (MxCo) (2.54), Maximal Crainocaudal (MxCr) (.61), Max CC (MxCc) (.34), Cormax LL (Comx) (.17), liver volume (calculated by formula) (Vcal) (2.02), CT Liver volumetry (VCt) (2.43). Distribution (p) is approximately normal for height (hgt) (.52), weight (wgt) (.15), Diaphragm to iliac (D-il) (.92), AP body dimension (ApBo) (.49), Transverse body dimension (TvBo) (.63), Maximal Ap (MxAp) (.81), Maximal Coronal (MxCo) (.12), Maximal Crainocaudal (MxCr) (.86), Max CC (MxCc) (.88), Cormax LL (Comx) (.37), liver volume (calculated by formula) (Vcal) (.44), CT Liver volumetry (VCt) (.30). The data does not follow a normal distribution (p) for: BMI (BMI) (.01).

Table 15 Central and dispersion parameters and measures of asymmetry and flatness for anthropometric and linear hepatic measurements in the group Sex-2 (85)

mean

min

max

hgt

166.66

7.10

150.0

183.0

4.26

165.13

168.19

.25

-.26

.418

wgt

70.18

10.70

50.0

105.0

15.26

67.87

72.49

.81

1.29

.168

BMI

25.26

3.43

17.3

36.3

13.60

24.52

26.00

.51

.54

.798

D-il

20.23

2.66

13.2

29.9

13.17

19.66

20.81

.44

.94

.768

ApBo

23.07

3.61

16.2

33.2

15.67

22.29

23.85

.40

.07

.991

TvBo

32.67

3.70

25.1

46.7

11.32

31.87

33.47

.70

1.70

.750

MxAp

16.01

2.04

12.3

20.7

12.75

15.57

16.46

.29

-.70

.288

MxCo

18.36

2.81

13.4

25.5

15.30

17.75

18.96

.46

-.41

.296

MxCr

16.55

1.94

12.6

21.3

11.72

16.13

16.97

.19

-.61

.852

MxCc

16.72

1.80

12.9

20.6

10.78

16.33

17.11

.21

-.76

.520

Comx

18.72

2.79

14.9

26.5

14.92

18.12

19.32

.74

-.22

.070

Vcal

1504.69

333.47

879.3

2451.6

22.16

1432.74

1576.63

.59

.02

.528

VCt

1455.49

302.02

853.2

2360.7

20.75

1390.33

1520.65

.51

-.08

.099

According to Minimal (min) and Maximal (max) values of anthropometric and linear hepatic measurements in the group Sex-2 we can say that values fall well within the expected range. The higher values of coefficient of variation (CV) mean that group Sex-2 is heterogenous in: liver volume (calculated by formula) (Vcal) (22.16) and CT Liver volumetry (VCt) (20.75). The values of coefficient of variation (CV) show homogenity for height (hgt) (4.26), weight (wgt) (15.26), BMI (BMI) (13.60), Diaphragm to iliac (D-il) (13.17), AP body dimension (ApBo) (15.67), Transverse body dimension (TvBo) (11.32), Maximal Ap (MxAp) (12.75), Maximal Coronal (MxCo) (15.30), Maximal Crainocaudal (MxCr) (11.72), Max CC (MxCc) (10.78), Cormax LL (Comx) (14.92). Increased values of Skewness (sk) show that distribution is negatively asymmetrical or Negatively Skewed Curve, This represents a frequency distribution in which comparatively more scores fall in higher classes, it has higher values than in the normal di: height (hgt) (.25), weight (wgt) (.81), BMI (BMI) (.51), Diaphragm to iliac (D-il) (.44), AP body dimension (ApBo) (.40), Transverse body dimension (TvBo) (.70), Maximal Ap (MxAp) (.29), Maximal Coronal (MxCo) (.46), Maximal Crainocaudal (MxCr) (.19), Max CC (MxCc) (.21), Cormax LL (Comx) (.74), liver volume (calculated by formula) (Vcal) (.59), CT Liver volumetry (VCt) (.51). The higher values of Kurtosis (k) indicate that curve is elongated for: weight (wgt) (1.29), BMI (BMI) (.54), Diaphragm to iliac (D-il) (.94), AP body dimension (ApBo) (.07), Transverse body dimension (TvBo) (1.70). A negative kurtosis (k) means that distribution is flatter than a normal curve for: height (hgt) (-.26), Maximal Ap (MxAp) (-.70), Maximal Coronal (MxCo) (-.41), Maximal Crainocaudal (MxCr) (-.61), Max CC (MxCc) (-.76), Cormax LL (Comx) (-.22), CT Liver volumetry (VCt) (-.08). Distribution (p) is approximately normal for height (hgt) (.42), weight (wgt) (.17), BMI (BMI) (.80), Diaphragm to iliac (D-il) (.77), AP body dimension (ApBo) (.99), Transverse body dimension (TvBo) (.75), Maximal Ap (MxAp) (.29), Maximal Coronal (MxCo) (.30), Maximal Crainocaudal (MxCr) (.85), Max CC (MxCc) (.52), liver volume (calculated by formula) (Vcal) (.53). The data does not follow a normal distribution (p) for: Cormax LL (Comx) (.07), CT Liver volumetry (VCt) (.10).

Analysis of the difference between genders for anthropometric and linear hepatic measurements

In this chapter we will accept or reject the hypothesis that there is significant difference between gender groups for anthropometric and linear hepatic measurements

Table 16 Significance of the difference between gender groups for anthropometric and linear hepatic measurements

Analysis

MANOVA

8.926

.000

Discriminant analysis

52790.730

.000

On the basis of values p = 0.000 ( MANOVA analysis) and p = .000 (Discriminant analysis) We rejected hypotheses H1 and H2 and accepted alternative hypotheses A1 and A2, it means that there is significant difference among genders.

Table 17 Significance of the difference between genders for anthropometric and linear hepatic measurements

Discrimination coefficient

hgt

39.560

.000

.673

wgt

28.285

.000

1.514

BMI

1.509

.219

.157

D-il

.637

.432

.003

ApBo

8.029

.005

.000

TvBo

4.174

.040

.009

MxAp

40.649

.000

.126

MxCo

.388

.542

.014

MxCr

.012

.879

.028

MxCc

.697

.410

.005

Comx

2.951

.084

.037

Vcal

8.586

.004

.000

VCt

14.045

.000

According to p <.1 we accepted alternative hypothesis A3. It means that there is a significant difference between gender groups for: height (.000), weight (.000), AP body dimension (.005), Transverse body dimension (.040), Maximal Ap (.000), Cormax LL (.084), liver volume (calculated by formula) (.004) and CT Liver volumetry (.000).

When p > .1 we accepted hypothesis H3. It means that there is no significant diference between genders for: BMI (.219), Diaphragm to iliac (.432), Maximal Coronal (.542), Maximal Crainocaudal (.879), Max CC (.410).

The amount of discrimination coefficient indicates that contribution to discrimination between genders for anthropometric and linear hepatic measurements is the highest, that is the difference is greatest for: weight (1.514), height (.673), BMI (.157), Maximal Ap (.126), Cormax LL (.037), Maximal Crainocaudal (.028), Maximal Coronal (.014), Transverse body dimension (.009), Max CC (.005), Diaphragm to iliac (.003), AP body dimension (.000), CT Liver volumetry (.000), liver volume (calculated by formula) (.000).

It should be noted, that latent variable is a variable for which no difference has been found between genders, but Discriminant Analysis has included it in the Structure by which there is a significant difference between genders.

The latent variables are: BMI (.219), Diaphragm to iliac (.432), Maximal Coronal (.542), Maximal Crainocaudal (.879), Max CC (.410).

Characteristics and homogenity of gender groups in relation to anthropometric and linear hepatic measurements

From the previous considerations and analyses of the sample consisting of 152 examinees, in accordance with the applied methodology, and if we follow the logical order of the research, now we should determine the characteristics and homogeneity of each gender group and the distance between them.

Based on p= 0.000, in discriminant analysis, we can conclude that there is a clearly defined border between gender groups, that is it is possible to determine the characteristics of each gender group for anthropometric and linear hepatic measurements.

Table 18 Characteristics and homogenity of gender groups in relation to anthropometric and linear hepatic measurements

Sex-1

Sex-2

dpr %

wgt

bigger* 1

less

59.002

hgt

bigger* 1

less

26.228

BMI

bigger

less

6.118

MxAp

bigger* 1

less

4.910

Comx

bigger* 1

less

1.442

MxCr

less

bigger

1.091

MxCo

less

bigger

.546

TvBo

bigger* 1

less

.351

MxCc

bigger

less

.195

D-il

bigger

less

.117

ApBo

bigger* 1

less

.000

VCt

bigger* 1

less

.000

Vcal

bigger* 1

less

.000

n/m

55/67

71/85

82.09

83.53

hmg – Homogenity; dpr % – contribution of a variable to the characteristics

The most defining for characteristics of each gender group is is weight because contribution of a variable to the characteristics is 59.00% then: height (26.23%), BMI (6.12%), Maximal Ap (4.91%), Cormax LL (1.44%), Maximal Crainocaudal (1.09%), Maximal Coronal (.55%), Transverse body dimension (.35%), Max CC (.19%), Diaphragm to iliac (.12%), AP body dimension (.00%), CT Liver volumetry (.00%) and liver volume (calculated by formula) (.00%). Homogenity, Sex-1 is 82.09% and Sex-2 is 83.53%.

From the presented facts we can conclude that Sex-1 have 55 from 67, Homogenity is 82.1% (bigger), it means that 12 examinees have characteristics that differ from the characteristics of the group they belong. The characteristics of the group Sex-2 have 71 from 85 examinees , Homogenity is 83.5% (bigger) because 14 examinees have different characteristics.

If someone has similar characteristics to characteristics of the group Sex-1 and we do not know their gender, we can expect with certanity 82.1% that they belong to the group Sex-1, or we can make prognosis with certain reliability.

Characteristics of the gender groups are:

– Sex-1: weight is bigger* 1, height is bigger* 1, BMI is bigger, Maximal Ap is bigger* 1, Cormax LL is bigger* 1, Maximal Crainocaudal is less, Maximal Coronal is less, Transverse body dimension is bigger* 1, Max CC is bigger, Diaphragm to iliac is bigger, AP body dimension is bigger* 1, CT Liver volumetry is bigger* 1, liver volume (calculated by formula) is bigger* 1.

– Sex-2: weight is less, height is less, BMI is less, Maximal Ap is less, Cormax LL is less, Maximal Crainocaudal is bigger, Maximal Coronal is bigger, Transverse body dimension is less, Max CC is less, Diaphragm to iliac is less, AP body dimension is less, CT Liver volumetry is less, liver volume (calculated by formula) is less.

Table 19 Mahalanobis distance between gender groups for anthropometric and linear hepatic measurements

Sex-1

Sex-2

Sex-1

.00

1.83

Sex-2

1.83

.00

By calculating Mahalanobis distance between gender groups we are obtaining another indicator of similarities or differences. Distances of different spaces can be compared. From the table we can say that the distance between gender groups: Sex-1 and Sex-2 is higher.

THE GROUP OF MALE EXAMINEES, FACTORS ANALYSIS

Analysis of structure of anthropometric and linear hepatic measurements

According to the previously established research plan for the structure of anthropometric and linear hepatic measurements, we planned to extract optimal number of factors using factor analysis of principal components from the data set consisted of 13 anthropometric and linear hepatic measurements in 67 male examinees. Anthropometric and linear hepatic measurements are: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal), CT Liver volumetry (VCt).

The aim is to find the associations between individual variables, to determine the contribution of each factor to a variable, to apply complementary analyses and to present the results Graphically. The coordinates of the variables for anthropometric and linear hepatic measurements will be presented to determine their position in an isolated structure.

In the table “Structure of isolated factors” columns are: inr – Inertia; F factor coordinate; cor- contribution of each factor to a variable; ctr- contribution of each variable to a factor. The results given in tables are multiplied by 1000.

Structure of 4 isolated factor for anthropometric and linear hepatic measurements

In this chapter we analysed the structure of four isolated factors (Principal Component Analysis) from 13 anthropometric and linear hepatic measurements: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal), CT Liver volumetry (VCt), on a sample of 67 male examinees.

Table 20 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

VCt

hgt

1000

wgt

373

1000

BMI

-565

521

1000

D-il

577

462

1000

ApBo

-127

610

612

439

1000

TvBo

-9

671

559

419

846

1000

MxAp

-30

380

358

233

670

519

1000

MxCo

103

-61

102

-37

-7

-116

1000

MxCr

366

364

395

226

112

202

255

1000

MxCc

336

468

153

487

335

249

297

195

933

1000

Comx

196

186

241

103

-44

722

231

243

1000

Vcal

273

458

182

408

460

339

543

519

829

809

437

1000

VCt

180

475

274

431

517

394

570

405

797

807

397

953

1000

We found the strongest correlations (953) between CT Liver volumetry (VCt) and liver volume (calculated by formula) (Vcal) and the strongest negative correlation is -565 between BMI (BMI) and height (hgt).

Table 21 The characteristic square of a factor and the percentage contribution

sqare

sum

5.556

42.741

2.673

20.561

63.302

1.445

11.117

74.419

1.118

8.597

83.016

.932

7.170

90.186

.431

3.316

93.502

.330

2.537

96.039

.260

2.004

98.042

.114

.875

98.918

.071

.545

99.463

.048

.369

99.832

.018

.140

99.972

.004

.028

100.000

Percentage representation of the characteristic squares fall in the range between .028% and 42.741%. The new structure is consisted of 4 isolated factors which contain 83.016% information from the whole sample.

Table 22 Structure of 4 isolated factors for anthropometric and linear hepatic measurements (group of 67 male examinees)

1 -factor

2 -factor

3 -factor

4 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

938

219

560

314

117

-510

260

180

562

316

282

wgt

883

736

541

-249

-144

510

260

232

BMI

809

464

215

-688

473

177

335

112

-95

D-il

514

645

416

-146

269

ApBo

835

713

508

-571

326

122

TvBo

802

640

409

-551

303

114

291

MxAp

618

601

361

-387

149

-171

-281

MxCo

873

313

560

313

117

678

460

318

MxCr

894

737

544

464

215

-279

-239

MxCc

868

807

651

117

333

111

-274

-175

Comx

849

382

146

474

225

633

400

277

278

Vcal

965

894

799

144

333

111

-233

VCt

945

906

820

148

221

-275

13.0

1000

The factor structure for anthropometric and linear hepatic measurements

Whole sample that consisted of 13 anthropometric and linear hepatic measurements is reduced to 4 isolated factors. Contribution of isolated factor (qlt) is significant for all 13 anthropometric and linear hepatic measurements.

* The communality is higher for: liver volume (calculated by formula) (Vcal) 965, CT Liver volumetry (VCt) 945, height (hgt) 938, Maximal Crainocaudal (MxCr) 894, weight (wgt) 883, Maximal Coronal (MxCo) 873, Max CC (MxCc) 868, Cormax LL (Comx) 849, AP body dimension (ApBo) 835, BMI (BMI) 809, Transverse body dimension (TvBo) 802, Maximal Ap (MxAp) 618.

* Intermediate communality shows that the structure of 4 isolated factors contain intermediate information about: Diaphragm to iliac (D-il) 514.

The variables that contribute in forming the structure of each isolated factor are: liver volume (calculated by formula), CT Liver volumetry, height, Maximal Crainocaudal, weight, Maximal Coronal, Max CC, Cormax LL, AP body dimension, BMI, Transverse body dimension, Maximal Ap, Diaphragm to iliac, the variables that do not contribute to factor structure are:

* Structure of the 1st- isolated factor is formed of 8 anthropometric and linear hepatic measurements: CT Liver volumetry (VCt) with factor contribution (cor) 821, liver volume (calculated by formula) (Vcal) 800, Max CC (MxCc) 651, Maximal Crainocaudal (MxCr) 544, weight (wgt) 542, AP body dimension (ApBo) 508, Diaphragm to iliac (D-il) 417, Transverse body dimension (TvBo) 410. Latent variables are: Maximal Ap (MxAp) 361. Association of CT Liver volumetry is in concordance with: liver volume (calculated by formula), Max CC, Maximal Crainocaudal, weight, AP body dimension, Diaphragm to iliac, Transverse body dimension, Maximal Ap.

* Structure of the 2nd- isolated factor is formed of 1 variable: BMI (BMI) with factor contribution (cor) 473. Latent variables are: AP body dimension (ApBo) 327, height (hgt) 314, Maximal Coronal (MxCo) 314, Transverse body dimension (TvBo) 304. Association of BMI is in concordance with: AP body dimension, Transverse body dimension. Association of BMI is inversely proportional with: height, Maximal Coronal.

* Structure of the 3rd- isolated factor is formed of 2 variables : Maximal Coronal (MxCo) with factor contribution (cor) 460, Cormax LL (Comx) 401. Association of Maximal Coronal is in concordance with: Cormax LL.

* Structure 4.- isolated factor is formed of 1 latent variable: height (hgt) with factor contribution (cor) 316.

* Several factors contribute to variable for: height, factor-2 (314), factor-4 (316), AP body dimension, factor-1 (508), factor-2 (327), Transverse body dimension, factor-1 (410), factor-2 (304), Maximal Coronal, factor-2 (314), factor-3 (460).

In forming the structure of 4 isolated factors contribute all 13 (100.00%) anthropometric and linear hepatic measurements.

Concordance of anthropometric and linear hepatic measurements and Structure of isolated factors

In forming the structure of 4 isolated factors 56 (83.58%) have high contribution, 7 (10.45%) have intermediate contribution, 4 are with low contribution without significance (5.97%).

1. – for 25 (37.31%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 12 (17.91%) examinees. For 17 examinees we found direct proportionality, and 20 examinees are inversely related.

2. – for 15 (22.39%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure are 7 (10.45%) examinees. For 13 examinees we found direct proportionality, and 9 examinees are inversely related.

3. – for 3 (4.48%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure are 6 (8.96%) examinees. For 7 examinees we found direct proportionality, and 2 examinees are inversely related.

4. – for 3 (4.48%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 4 isolated factor. Latently related to the structure are 2 (2.99%) examinees. For 2 examinees we found direct proportionality, and 3 examinees are inversely related.

The concordance of anthropometric and linear hepatic measurements with the structure: two and more factor have 1 examinee, one factor have 44 examinees, latent agreement only have 15 examinees, with no agreement are 7 examinees.

It should be noted that 3 examinees stand out from the rest (inr).

Graph 13 Graphicalal representation of anthropometric and linear hepatic measurements in the isolated factors structures

Graph 14 Graphicalal representation of anthropometric and linear hepatic measurements in the isolated factors structures 1F and 2F

Graph 15 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structures 1F and 3F

Graph 16 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structures 2F and 3F

FACTORS ANALYSIS FOR FEMALE GROUP

Analysis of the structure of anthropometric and linear hepatic measurements

According to the previously established research plan for the structure of anthropometric and linear hepatic measurements, we planned to extract optimal number of factors using factor analysis of principal components from the data set consisted of 13 anthropometric and linear hepatic measurements in 85 female examinees. Anthropometric and linear hepatic measurements are: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal), CT Liver volumetry (VCt).

The aim is to find the associations of individual variables, to determine the contribution of each factor to a variable, to determine contribution of each variable to a factor, to apply complementary analyses and to present the results Graphically. The coordinates of the variables for anthropometric and linear hepatic measurements will be presented to determine their position in an isolated structure.

Structure 4 isolated factor for anthropometric and linear hepatic measurements

In this chapter we analysed the structure 4 isolated factors (Principal Component Analysis) from 13 anthropometric and linear hepatic measurements: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal), CT Liver volumetry (VCt), on a sample of 85 female examinees.

Table 23 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

VCt

hgt

1000

wgt

448

1000

BMI

-135

822

1000

D-il

264

272

1000

ApBo

-38

517

614

207

1000

TvBo

638

706

377

776

1000

MxAp

162

469

436

296

569

425

1000

MxCo

242

-67

-20

-19

-134

1000

MxCr

-104

-133

175

115

120

-72

1000

MxCc

236

290

279

149

165

870

1000

Comx

199

-21

165

-26

845

153

1000

Vcal

228

255

143

307

393

311

443

641

532

671

592

1000

VCt

162

248

178

326

416

298

446

492

513

647

476

883

1000

We found the strongest correlations (883) between CT Liver volumetry (VCt) and liver volume (calculated by formula) (Vcal) and the strongest negative correlation is -135 between BMI (BMI) and height (hgt).

Table 24 The characteristic square of a factor and the percentage contribution

sqare

sum

4.625

35.575

2.850

21.924

57.499

1.782

13.707

71.206

1.082

8.327

79.533

.834

6.415

85.948

.816

6.275

92.222

.427

3.288

95.510

.192

1.474

96.984

.157

1.205

98.189

.131

1.010

99.199

.096

.740

99.940

.006

.046

99.986

.002

.014

100.000

Percentage representation of the characteristic squares fall in the range between .014% and 35.575%. The new structure is consisted of 4 isolated factors which contain 79.533 % information from the whole sample.

Table 25 Structure of 4 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

4 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

962

-245

131

-428

183

103

838

702

649

wgt

864

-626

392

-535

287

101

-341

116

264

BMI

845

-548

301

-688

473

166

-112

-244

D-il

248

-486

236

-81

-52

ApBo

743

-699

488

106

-458

209

132

-168

TvBo

768

-693

480

104

-516

266

-125

MxAp

546

-593

352

-399

159

-7

187

MxCo

930

-396

157

615

379

133

-582

338

190

-238

MxCr

894

-425

181

485

236

678

460

258

132

MxCc

897

-632

400

402

161

566

320

179

128

Comx

889

-424

179

558

311

109

-567

321

180

-279

Vcal

927

-849

721

156

452

204

-24

-23

VCt

825

-824

678

147

375

141

-29

13.0

1000

The factor structure of anthropometric and linear hepatic measurements in female group

Whole sample consisted of 13 anthropometric and linear hepatic measurements is reduced to 4 isolated factors. Contribution of isolated factor (qlt) is significant for 12 anthropometric and linear hepatic measurements.

* The communality is higher for: height (hgt) 962, Maximal Coronal (MxCo) 930, liver volume (calculated by formula) (Vcal) 927, Max CC (MxCc) 897, Maximal Crainocaudal (MxCr) 894, Cormax LL (Comx) 889, weight (wgt) 864, BMI (BMI) 845, CT Liver volumetry (VCt) 825, Transverse body dimension (TvBo) 768, AP body dimension (ApBo) 743.

* Intermediate communality shows that the structure of 4 isolated factors contain intermediate information about 1 anthropometric and linear hepatic measurement: Maximal Ap (MxAp) 546.

* Decreased communality shows that the structure of 4 isolated factors does not contain enough information about 1 anthropometric and linear hepatic measurement: Diaphragm to iliac (D-il) 248

The variables that contribute in forming the structure of each isolated factor are: height, Maximal Coronal, liver volume (calculated by formula), Max CC, Maximal Crainocaudal, Cormax LL, weight, BMI, CT Liver volumetry, Transverse body dimension, AP body dimension, Maximal Ap, the variable that do not contribute to factor structure are: Diaphragm to iliac.

* Structure of the 1st- isolated factor is formed of 5 anthropometric and linear hepatic measurements: liver volume (calculated by formula) (Vcal) with factor contribution (cor) 722, CT Liver volumetry (VCt) 679, AP body dimension (ApBo) 489, Transverse body dimension (TvBo) 481, Max CC (MxCc) 400. Latent variables are: weight (wgt) 392, Maximal Ap (MxAp) 352, BMI (BMI) 301. Association liver volume (calculated by formula) is in concordance with: CT Liver volumetry, AP body dimension, Transverse body dimension, Max CC, weight, Maximal Ap, BMI.

* Structure of the 2nd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: BMI (BMI) with factor contribution (cor) 473. Latent variables are: Maximal Coronal (MxCo) 379, Cormax LL (Comx) 312, weight (wgt) 287. Association of BMI is in concordance with: weight. Association of BMI is inversely proportional with: Maximal Coronal, Cormax LL.

* Structure of the 3rd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: Maximal Crainocaudal (MxCr) with factor contribution (cor) 460. Latent variables are: Maximal Coronal (MxCo) 339, Cormax LL (Comx) 322, Max CC (MxCc) 320. Association of Maximal Crainocaudal is in concordance with: Max CC. Association Maximal Crainocaudal is inversely proportional with: Maximal Coronal, Cormax LL.

* Structure 4.- isolated factor is formed of 1 anthropometric and linear hepatic measurement: height (hgt) with factor contribution (cor) 703.

* Several factors contribute to variable for: weight, factor-1 (392), factor-2 (287), BMI, factor-1 (301), factor-2 (473), Maximal Coronal, factor-2 (379), factor-3 (339), Max CC, factor-1 (400), factor-3 (320), Cormax LL, factor-2 (312), factor-3 (322).

In forming the structure of two and more factors 5 anthropometric and linear hepatic measurements contribute the most, in forming only one factor contribute 7 anthropometric and linear hepatic measurements, 1 bbb1 has no influence in forming the factors structure

In forming the structure of isolated factors contribute 12 (92.31%) anthropometric and linear hepatic measurements.

Concordance of anthropometric and linear hepatic measurements and Structure of isolated factors

In forming the structure of 4 isolated factors from the sammple consisting of 85 examinees 68 (80.00%) examinees have high contribution, 13 (15.29%) examinees have intermediate contribution, with low contribution without significance are 4 (4.71%).

1. – for 29 examinees (34.12%) anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 8 (9.41%) examinees. For 22 examinees we found direct proportionality, and 15 examinees were inversely related.

2. – for 18 (21.18%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure are 12 (14.12%) examinees. For 17 examinees we found direct proportionality, and 13 examinees are inversely related.

3. – for 9 (10.59%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure for 6 (7.06%) examinees. For 8 we found direct proportionality, and 7 are inversely related.

4. – for 3 (3.53%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 4 isolated factor. Latently related to the structure are 8 (9.41%) examinees. For 8 examinees we found direct proportionality, and 3 examinees are inversely related.

The concordance of anthropometric and linear hepatic measurements with the structure: one factor have 59 examinees , latent agreement only have 17 examinees, with no agreement are 9 examinees.

It should be noted that 1 examinee stands out from the rest (inr)

Graph 17 Graphicalal representation of anthropometric and linear hepatic measurements in the isolated factor structures

Graph 18 Graphicalal representation of anthropometric and linear hepatic measurements in the isolated factor structures 1F and 2F

Graph 19 Graphicalal representation of anthropometric and linear hepatic measurements in the isolated factor structures 1F and 3F

Graph 20 Graphicalal representation of anthropometric and linear hepatic measurements in the isolated factors structures 2F and 3F

AGE RELATED DIFFERENCES

In this part of the study we will analyse anthropometric and linear hepatic measurements by age groups.

AGE GROUPS

In accordance to the previously established design of the study including 106 we will analyse age-related changes in anthropometric and linear hepatic measurements. In the first part of this chapter we will show descriptive statistics: Central and dispersion parameters and measures of asymmetry and flatness for three age groups. In the second part we will analyse differences between age groups, ie hypotheses will be accepted or rejected, in order to assess the results and the usefulness of further analysis, determine the directions and methodological priorities. If the conditions are met, we will define the characteristics and homogeneity of each age group, and determine the distance between them. The results will be presented Graphically.

We will analyse anthropometric and linear hepatic measurements by age, The sample consisting of 152 examinees, will be divided into three age groups: 18-47 (26), 48-65 (70), 66-86 (56).

Central and dispersion parameters, measures of asymmetry and flatness of variables investigated (anthropometric and linear hepatic measurements) represent age groups and we are investigating the possibility of applying parametric procedures.

Table 1 Central and dispersion parameters and measures of asymmetry and flatness for the anthropometric and linear hepatic measurements for three age groups: 18-47 (26) od 48-65 (70), (age 66-86) (56)

mean

min

max

:: strG-1

36.27

8.67

19.0

47.0

23.92

32.76

39.77

-.40

-1.01

.920

:: strG-2

57.96

5.13

48.0

65.0

8.85

56.73

59.18

-.42

-1.02

.600

:: strG-3

72.66

4.84

66.0

83.0

6.66

71.36

73.96

.28

-1.13

.401

Analysis of differences between age groups for anthropometric and linear hepatic measurements

In accordance to the previously established design of the study including 106 we will analyse anthropometric and linear hepatic measurements among the age groups. In the first part we will show Central and dispersion parameters and measures of asymmetry and flatness. In the second part we will analyse differences between age groups, hypotheses will be accepted or rejected, in order to assess the results and the usefulness of further analysis, determine the directions and methodological priorities. If the conditions are met, we will define the characteristics and homogeneity of each age group, and determine the distance between them. The results will be presented Graphically.

We will analyse anthropometric and linear hepatic measurements: height, weight, BMI, Diaphragm to iliac, AP body dimension, Transverse body dimension, Maximal Ap, Maximal Coronal, Maximal Crainocaudal, Max CC, Cormax LL, liver volume (calculated by formula), CT Liver volumetry, The sample consisted of 152 examinees. They are divided in 3 groups by age: 18-47 (26), 48-65 (70), 66-86 (56),

Descriptive statistics for anthropometric and linear hepatic measurements in the age groups

Central and dispersion parameters, measures of asymmetry and flatness for anthropometric and linear hepatic measurements are presented for all age groups and we are investigating the possibility of applying parametric procedures.

Table 9 Central and dispersion parameters and measures of asymmetry and flatness of anthropometric and linear hepatic measurements for the group of young examinees (age 18-47) (26)

mean

min

max

hgt

175.58

10.02

153.0

197.0

5.70

171.53

179.62

-.16

-.04

.864

wgt

74.69

14.69

53.0

120.0

19.67

68.76

80.63

1.26

1.77

.344

BMI

24.16

3.64

17.3

31.9

15.09

22.68

25.63

.54

-.41

.370

D-il

21.83

2.87

16.3

30.8

13.16

20.66

22.99

.85

2.01

.943

ApBo

22.65

4.18

16.2

35.8

18.44

20.96

24.34

1.21

1.98

.511

TvBo

32.54

3.47

27.1

41.8

10.68

31.13

33.94

.88

.25

.180

MxAp

16.22

2.17

13.7

22.9

13.36

15.35

17.10

1.26

1.47

.089

MxCo

19.67

2.64

15.6

26.

13.41

18.60

20.74

.75

.31

.870

MxCr

17.60

2.41

14.7

25.1

13.71

16.62

18.57

1.48

2.24

.319

MxCc

17.70

2.36

14.9

24.4

13.31

16.75

18.65

1.18

1.15

.611

Comx

20.80

2.59

16.6

26.8

12.44

19.75

21.84

.62

.00

.777

Vcal

1748.42

464.66

1175.5

3385.5

26.58

1560.69

1936.14

1.69

3.90

.558

VCt

1654.10

417.95

1080.0

3092.2

25.27

1485.25

1822.95

1.50

3.39

.695

A note: The values of asymmetry and flatnessu are between -.04 do .04 were not discussed

Minimal (min) and Maximal (max) values of anthropometric and linear hepatic measurements in the group of young examinees (age 18-47) fall well within the expected range of values. The higher values of the coefficient of variation (CV) show heterogenity for some variables in the group of young (age 18-47): liver volume (calculated by formula) (Vcal) (26.58), CT Liver volumetry (VCt) (25.27). The values of coefficient of variation (CV) show homogenity for: height (hgt) (5.70), weight (wgt) (19.67), BMI (BMI) (15.09), Diaphragm to iliac (D-il) (13.16), AP body dimension (ApBo) (18.44), Transverse body dimension (TvBo) (10.68), Maximal Ap (MxAp) (13.36), Maximal Coronal (MxCo) (13.41), Maximal Crainocaudal (MxCr) (13.71), Max CC (MxCc) (13.31), Cormax LL (Comx) (12.44). Increased values of Skewness (sk) show that distribution is negatively asymmetrical or Negatively Skewed Curve. This represents a frequency distribution in which comparatively more scores fall in higher classes, it has higher values than in the normal distribution: weight (wgt) (1.26), BMI (BMI) (.54), Diaphragm to iliac (D-il) (.85), AP body dimension (ApBo) (1.21), Transverse body dimension (TvBo) (.88), Maximal Ap (MxAp) (1.26), Maximal Coronal (MxCo) (.75), Maximal Crainocaudal (MxCr) (1.48), Max CC (MxCc) (1.18), Cormax LL (Comx) (.62), liver volume (calculated by formula) (Vcal) (1.69), CT Liver volumetry (VCt) (1.50). Decreased values of Skewness (sk) show that distribution is positively asymmetrical or Positively Skewed Curve. Such a curve results from a frequency distribution where observation concentrate in lower classes, it has more lower values compared to normal height (hgt) (-.16). The higher values of Kurtosis (k) indicate that curve is elongated for: weight (wgt) (1.77), Diaphragm to iliac (D-il) (2.01), AP body dimension (ApBo) (1.98), Transverse body dimension (TvBo) (.25), Maximal Ap (MxAp) (1.47), Maximal Coronal (MxCo) (.31), Maximal Crainocaudal (MxCr) (2.24), Max CC (MxCc) (1.15), liver volume (calculated by formula) (Vcal) (3.90), CT Liver volumetry (VCt) (3.39). A negative kurtosis (k) means that distribution is flatter than a normal curve for: BMI (BMI) (-.41). Distribution (p) is approximately normal for height (hgt) (.86), weight (wgt) (.34), BMI (BMI) (.37), Diaphragm to iliac (D-il) (.94), AP body dimension (ApBo) (.51), Transverse body dimension (TvBo) (.18), Maximal Coronal (MxCo) (.87), Maximal Crainocaudal (MxCr) (.32), Max CC (MxCc) (.61), Cormax LL (Comx) (.78), liver volume (calculated by formula) (Vcal) (.56), CT Liver volumetry (VCt) (.69). The data does not follow a normal distribution (p) for: Maximal Ap (MxAp) (.09).

Table 10 Central and dispersion parameters and measures of asymmetry and flatness of anthropometric and linear hepatic measurements for the group of middle-aged examinees (age 48-65) (70)

mean

min

max

hgt

170.07

10.89

117.0

190.0

6.40

167.48

172.67

-1.55

6.50

.674

wgt

74.71

12.87

50.0

105.0

17.23

71.64

77.78

.24

-.35

.857

BMI

26.00

5.43

18.8

57.0

20.86

24.71

27.30

2.88

13.55

.015

D-il

20.66

2.83

14.8

29.9

13.70

19.98

21.33

.44

.15

.651

ApBo

23.84

4.27

16.2

34.9

17.90

22.82

24.85

.38

-.26

.687

TvBo

33.30

4.19

25.1

46.7

12.59

32.30

34.30

.48

.59

.883

MxAp

16.82

2.47

12.3

21.4

14.67

16.23

17.41

-.07

-1.03

.704

MxCo

18.28

2.49

13.4

25.5

13.65

17.68

18.87

.91

.89

.027

MxCr

17.07

2.00

11.6

21.3

11.69

16.59

17.54

-.01

-.29

.580

MxCc

17.28

1.94

12.3

21.7

11.23

16.82

17.75

.01

-.44

.879

Comx

18.92

2.47

14.9

26.2

13.03

18.34

19.51

.64

.10

.652

Vcal

1622.14

359.48

939.3

2574.4

22.16

1536.41

1707.88

.47

-.24

.693

VCt

1566.18

318.22

853.2

2437.8

20.32

1490.29

1642.08

.42

-.12

.169

Minimal (min) and Maximal (max) values of anthropometric and linear hepatic measurements in the group of middle-aged examinees (age 48-65) fall well within the expected range of values. The higher values of coefficient of variation (CV) show heterogenity in the group of middle-aged examinees for: BMI (BMI) (20.86), liver volume (calculated by formula) (Vcal) (22.16), CT Liver volumetry (VCt) (20.32). The values of coefficient of variation (CV) show heterogenity for: height (hgt) (6.40), weight (wgt) (17.23), Diaphragm to iliac (D-il) (13.70), AP body dimension (ApBo) (17.90), Transverse body dimension (TvBo) (12.59), Maximal Ap (MxAp) (14.67), Maximal Coronal (MxCo) (13.65), Maximal Crainocaudal (MxCr) (11.69), Max CC (MxCc) (11.23), Cormax LL (Comx) (13.03). Increased values of Skewness (sk) show that distribution is negatively asymmetrical or Negatively Skewed Curve. This represents a frequency distribution in which comparatively more scores fall in higher classes, it has higher values than in the normal distribution for: weight (wgt) (.24), BMI (BMI) (2.88), Diaphragm to iliac (D-il) (.44), AP body dimension (ApBo) (.38), Transverse body dimension (TvBo) (.48), Maximal Coronal (MxCo) (.91), Cormax LL (Comx) (.64), liver volume (calculated by formula) (Vcal) (.47), CT Liver volumetry (VCt) (.42). Decreased values of Skewness (sk) show that distribution is positively asymmetrical or positively Skewed Curve. Such a curve results from a frequency distribution where observation concentrate in lower classes, it has more lower values compared to normal height (hgt) (-1.55), Maximal Ap (MxAp) (-.07). According to values of Skewness (s) we can say that distribution is not asymmetrical for: Maximal Crainocaudal (MxCr) (-.01), Max CC (MxCc) (.01). The higher values of Kurtosis (k) indicate that curve is elongated for: height (hgt) (6.50), BMI (BMI) (13.55), Diaphragm to iliac (D-il) (.15), Transverse body dimension (TvBo) (.59), Maximal Coronal (MxCo) (.89), Cormax LL (Comx) (.10). A negative kurtosis (k) means that distribution is flatter than a normal curve for: weight (wgt) (-.35), AP body dimension (ApBo) (-.26), Maximal Ap (MxAp) (-1.03), Maximal Crainocaudal (MxCr) (-.29), Max CC (MxCc) (-.44), liver volume (calculated by formula) (Vcal) (-.24), CT Liver volumetry (VCt) (-.12). Distribution (p) is approximately normal for height (hgt) (.67), weight (wgt) (.86), Diaphragm to iliac (D-il) (.65), AP body dimension (ApBo) (.69), Transverse body dimension (TvBo) (.88), Maximal Ap (MxAp) (.70), Maximal Crainocaudal (MxCr) (.58), Max CC (MxCc) (.88), Cormax LL (Comx) (.65), liver volume (calculated by formula) (Vcal) (.69), CT Liver volumetry (VCt) (.17). The data does not follow a normal distribution (p) for: BMI (BMI) (.01), Maximal Coronal (MxCo) (.03).

Table 11 Central and dispersion parameters and measures of asymmetry and flatness for anthropometric and linear hepatic measurements in the group of old examinees (age 66-86) (56)

mean

min

max

hgt

169.61

9.32

150.0

195.0

5.49

167.11

172.10

.40

-.12

.628

wgt

74.66

12.02

59.0

120.0

16.10

71.44

77.88

1.56

3.14

.025

BMI

25.90

2.97

21.6

35.9

11.48

25.10

26.69

.99

1.26

.338

D-il

19.41

2.79

13.2

25.8

14.39

18.66

20.16

.10

-.00

.776

ApBo

24.41

3.10

18.4

34.2

12.69

23.58

25.24

.99

1.53

.546

TvBo

33.43

3.24

28.5

44.5

9.68

32.56

34.30

.91

1.33

.715

MxAp

17.52

2.19

13.0

24.0

12.48

16.94

18.11

.48

.72

.774

MxCo

17.54

2.43

13.6

23.5

13.86

16.89

18.19

.54

-.41

.431

MxCr

15.37

2.19

11.6

22.9

14.27

14.78

15.95

.81

.98

.133

MxCc

15.92

2.13

12.0

24.0

13.36

15.35

16.49

1.09

2.16

.597

Comx

18.39

2.65

14.9

24.8

14.39

17.68

19.10

.81

-.35

.124

Vcal

1475.02

423.48

879.3

3220.1

28.71

1361.58

1588.45

1.71

4.00

.103

VCt

1483.36

393.54

931.9

3092.3

26.53

1377.95

1588.78

1.67

3.83

.092

Minimal (min) and Maximal (max) values of anthropometric and linear hepatic measurements in the group of old examinees (age 66-86) fall well within the expected range of values. Higher values of the coefficient of variation (CV) show heterogenity in the group of old examinees (age 66-86) for: liver volume (calculated by formula) (Vcal) (28.71), CT Liver volumetry (VCt) (26.53). The values of coefficient of variation (CV) show homogenity for height (hgt) (5.49), weight (wgt) (16.10), BMI (BMI) (11.48), Diaphragm to iliac (D-il) (14.39), AP body dimension (ApBo) (12.69), Transverse body dimension (TvBo) (9.68), Maximal Ap (MxAp) (12.48), Maximal Coronal (MxCo) (13.86), Maximal Crainocaudal (MxCr) (14.27), Max CC (MxCc) (13.36), Cormax LL (Comx) (14.39). Increased values of Skewness (sk) show that distribution is negatively asymmetrical or Negatively Skewed Curve, This represents a frequency distribution in which comparatively more scores fall in higher classes, it has higher values than in the normal distribution for: height (hgt) (.40), weight (wgt) (1.56), BMI (BMI) (.99), Diaphragm to iliac (D-il) (.10), AP body dimension (ApBo) (.99), Transverse body dimension (TvBo) (.91), Maximal Ap (MxAp) (.48), Maximal Coronal (MxCo) (.54), Maximal Crainocaudal (MxCr) (.81), Max CC (MxCc) (1.09), Cormax LL (Comx) (.81), liver volume (calculated by formula) (Vcal) (1.71), CT Liver volumetry (VCt) (1.67). The higher values of Kurtosis (k) indicate that curve is elongated for: weight (wgt) (3.14), BMI (BMI) (1.26), AP body dimension (ApBo) (1.53), Transverse body dimension (TvBo) (1.33), Maximal Ap (MxAp) (.72), Maximal Crainocaudal (MxCr) (.98), Max CC (MxCc) (2.16), liver volume (calculated by formula) (Vcal) (4.00), CT Liver volumetry (VCt) (3.83). A negative kurtosis (k) means that distribution is flatter than a normal curve for: height (hgt) (-.12), Maximal Coronal (MxCo) (-.41), Cormax LL (Comx) (-.35). Distribution (p) is approximately normal for height (hgt) (.63), BMI (BMI) (.34), Diaphragm to iliac (D-il) (.78), AP body dimension (ApBo) (.55), Transverse body dimension (TvBo) (.71), Maximal Ap (MxAp) (.77), Maximal Coronal (MxCo) (.43), Maximal Crainocaudal (MxCr) (.13), Max CC (MxCc) (.60), Cormax LL (Comx) (.12), liver volume (calculated by formula) (Vcal) (.10). The data does not follow a normal distribution (p) for: weight (wgt) (.03), CT Liver volumetry (VCt) (.09).

Analysis of differences between age groups for anthropometric and linear hepatic measurements

In this chapter we will accept or reject the hypothesis that there is significant difference between age groups for anthropometric and linear hepatic measurements

Table 12 Significance of the difference between age groups for anthropometric and linear hepatic measurements

Analysis

MANOVA

3.424

.000

discriminativna

99999.990

.000

From values p = .000 (MANOVA analysis) and p = .000 (discriminant analysis), we rejected hypotheses H1 and H2 and we accepted alternative hypothesis A1 and alternative hypothesis A2, this means that there is a significant difference and a clearly defined boundary between the age groups.

Table 13 Significance of the difference between age groups for anthropometric and linear hepatic measurements

discrimination coefficient

hgt

3.421

.035

4.687

wgt

.000

1.000

3.792

BMI

1.831

.164

.178

D-il

7.029

.001

.235

ApBo

1.842

.162

.005

TvBo

.536

.586

.004

MxAp

3.094

.048

4.716

MxCo

6.503

.002

2.410

MxCr

13.671

.000

1.378

MxCc

9.259

.000

.025

Comx

8.054

.000

.025

Vcal

4.515

.012

.000

VCt

2.057

.131

.000

Since p <.1 we accepted alternative hypothesis A3, this means that there is a significant difference between some of the age groups for: height (.035), Diaphragm to iliac (.001), Maximal Ap (.048), Maximal Coronal (.002), Maximal Crainocaudal (.000), Max CC (.000), Cormax LL (.000), liver volume (calculated by formula) (.012).

When p > .1 we accepted hypothesis H3, this means that there is no significant difference between age groups for: weight (1.000), BMI (.164), AP body dimension (.162), Transverse body dimension (.586), CT Liver volumetry (.131).

Discrimination coefficient shows that contribution to discrimination between age groups is the highest, that is a difference is greatest for: Maximal Ap (4.716), height (4.687), weight (3.792), Maximal Coronal (2.410), Maximal Crainocaudal (1.378), Diaphragm to iliac (.235), BMI (.178), Max CC (.025), Cormax LL (.025), AP body dimension (.005), Transverse body dimension (.004), liver volume (calculated by formula) (.000), CT Liver volumetry (.000).

It should be noted that latent variable is a variable that showed no significant age difference, but discriminant analysis has included it in the structure which shows significant age difference.

Latent variables are: weight (1.000), BMI (.164), AP body dimension (.162), Transverse body dimension (.586), CT Liver volumetry (.131).

Characteristics and Homogenity for the anthropometric and linear hepatic measurements in three age groups

From the previous considerations and analyses of the sample of 152 examinees divided into three age groups, in accordance with the applied methodology, and if we follow the logical order of the research, now we should determine the characteristics and homogeneity of each age group and the distance between them.

Based on p= .000 from discriminant analysis, we can conclude that there is a clearly defined border between age groups, that is it is possible to determine the characteristics of each age group for anthropometric and linear hepatic measurements.

Table 14 Characteristics and Homogenity of the age groups for anthropometric and linear hepatic measurements

Age

18-47

48-65

66-86

contribution %

MxAp

less

intermediate

bigger* 2

27.018

hgt

bigger* 2

intermediate

less

26.852

wgt

intermediate

bigger

less

21.724

MxCo

bigger* 2

intermediate* 1

less

13.807

MxCr

bigger* 1

intermediate* 1

less

7.895

D-il

bigger* 2

intermediate* 1

less

1.346

BMI

less

bigger

intermediate* 1

1.020

MxCc

bigger* 1

intermediate* 1

less

.143

Comx

bigger* 2

intermediate

less

.143

ApBo

less

intermediate

bigger* 1

.029

TvBo

less

intermediate

bigger

.023

Vcal

bigger* 1

intermediate* 1

less

.000

VCt

bigger* 1

intermediate

less

.000

n/m

21/26

43/70

43/56

80.77

61.43

76.79

Contribution % – contribution of a variable to the characteristics

The most defining for characteristics of each age group is Maximal Ap because contribution of a variable to the characteristics is 27.02% then: height (26.85%), weight (21.72%), Maximal Coronal (13.81%), Maximal Crainocaudal (7.89%), Diaphragm to iliac (1.35%), BMI (1.02%), Max CC (.14%), Cormax LL (.14%), AP body dimension (.03%), Transverse body dimension (.02%), liver volume (calculated by formula) (.00%) and CT Liver volumetry (.00%). Homogenity, (age 18-47) je 80.77%, (age 48-65) is 61.43% and (age 66-86)je 76.79%.

From the facts presented we can conclude that characteristics of the young have 21 from 26 examinees, Homogenity is 80.8% (bigger), this means that 5 examinees have different characteristics (different from the group they belong), characteristics of the middle-aged group have 43 from 70 examinees, homogenity is 61.4% (bigger) because 27 examinees have different characteristics, characteristics of the group of old people have 43 od 56 examinees, Homogenity is 76.8% (bigger) because 13 examinees have different characteristics.

If someone has similar characteristics to the group of young (age 18-47), and we do not know their age, we can expect with certanity of 80.8% that they belong to the group of young (age 18-47), we can make prognosis with certain reliability.

Characteristics of the age groups are:

– Age 18-47: for Maximal Ap is less, for height is bigger* 2, for weight is intermediate, for Maximal Coronal is bigger* 2, for Maximal Crainocaudal is bigger* 1, for Diaphragm to iliac is bigger* 2, for BMI is less, for Max CC is bigger* 1, for Cormax LL is bigger* 2, for AP body dimension is less, for Transverse body dimension is less, for liver volume (calculated by formula) is bigger* 1, for CT Liver volumetry is bigger* 1.

– od 48-65 have svojstva, for Maximal Ap is intermediate, for height is intermediate, for weight is bigger, for Maximal Coronal is intermediate* 1, for Maximal Crainocaudal is intermediate* 1, for Diaphragm to iliac is intermediate* 1, for BMI is bigger, for Max CC is intermediate* 1, for Cormax LL is intermediate, for AP body dimension is intermediate, for Transverse body dimension is intermediate, for liver volume (calculated by formula) is intermediate* 1, for CT Liver volumetry is intermediate.

– (age 66-86) have svojstva, for Maximal Ap is bigger* 2, for height is less, for weight is less, for Maximal Coronal is less, for Maximal Crainocaudal is less, for Diaphragm to iliac is less, for BMI is intermediate* 1, for Max CC is less, for Cormax LL is less, for AP body dimension is bigger* 1, for Transverse body dimension is bigger, for liver volume (calculated by formula) is less, for CT Liver volumetry is less.

Table 15 Mahalanobis distance between age groups in relation to anthropometric and linear hepatic measurements

Age

18-47

48-65

66-86

18-47g

.00

1.28

2.13

48-65g

1.28

.00

1.25

66-86g

2.13

1.25

.00

By calculating Mahalanobis distance between age groups we are obtaining another indicator of similarities or differences. Distances of different spaces can be compared. From the table we can say that the distances between age groups are: for old (age 66-86) and middle-aged (age 48-65) groups is 1.25, the farthest are age groups: of old ( age 66-86) and young (age 18-47) with the distance 2.13 (bigger).

Table 16 Grouping of the age groups for anthropometric and linear hepatic measurements

level

closeness

48-65g,66-86g

1.25

18-47g,48-65g

1.71

From the dendrogram shown we can see that groups of middle-aged and old are the closest with the distance of 1.25. The biggest difference is between 18-47 and 48-65, with the distance 1.71. nije isto kao Mahalanobis?

Legend: 18-47 (1) 48-65 (2) 66-86 (3)

Graphicalal representation of differences between age groups for 3 the most discriminatory variables

From the Graphical representation using ellipses (confidence interval) we can see correlative positions and characteristics of each age group: age 18-47 (1), age 48-65 (2), age 66-86 (3), for the 3 the most discriminatory variable: Maximal Ap (MxAp), height (hgt), weight (wgt).

Graph 3 Ellipses (confidence interval) for the age groups, Maximal Ap and height

Legend: age 18-47 (1); age 48-65 (2); age 66-86 (3);; Maximal Ap (MxAp); height (hgt)

As shown on the graph (3) abscissa (horizontal axis) is Maximal Ap (MxAp), ordinate (vertical axis) is height (hgt).

We can notice that for Maximal Ap, group of young (age 18-47) (1) have the lowest value, while the group of old 66-86 (3) has the highest value. The values of height are the lowest in the group of old (age 66-86) (3), and the highest in the group of young examinees (age 18-47) (1).

Graph 4 Ellipses (confidence interval) for the groups, Maximal Ap and weight

Legend: od 18-47 (1); age 48-65 (2); age 66-86 (3);; Maximal Ap (MxAp); weight (wgt)

As shown on the graph (4) abscissa (horizontal axis) is Maximal Ap (MxAp), ordinate (vertical axis) is weight (wgt).

We can notice that for Maximal Ap, group of young examinees (age 18-47) (1) have the lowest values, while it has the highest value in the group of old examinees (age 66-86) (3). The values of weight, are the lowest in the group of old persons (age 66-86) (3), and the highest in the group of middle-aged 48-65 (2).

Graph 5 Ellipses (confidence interval), age groups for height and weight

Legend: age 18-47 (1); age 48-65 (2); age 66-86 (3);; height (hgt); weight (wgt)

As shown on the graph (5) abscissa (horizontal axis)je height (hgt), ordinate (vertical axis) is weight (wgt).

We can notice that that the values of height are the lowest in the group of old (age 66-86) (3), while height has the highest value in the group of young (age 18-47) (1). The values of weight are the lowest in the froup of old (age 66-86) (3), and the highest in the group od middle-aged individuals 48-65 (2).

THE FACTOR STRUCTURE

Group of young examinees (age 18-47) (26) structure

In this chapter we analysed the structure of 4 isolated factors (Principal Component Analysis) from 13 anthropometric and linear hepatic measurements: Maximal Ap (MxAp), height (hgt), weight (wgt), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Diaphragm to iliac (D-il), BMI (BMI), Max CC (MxCc), Cormax LL (Comx), AP body dimension (ApBo), Transverse body dimension (TvBo), liver volume (calculated by formula) (Vcal), CT Liver volumetry (VCt). The sample consisted of 152 examinees.

Table 17 The correlation matrix

MxAp

hgt

wgt

MxCo

MxCr

D-il

BMI

MxCc

Comx

ApBo

TvBo

Vcal

VCt

MxAp

1000

hgt

251

1000

wgt

528

508

1000

MxCo

-135

121

1000

MxCr

207

147

142

1000

D-il

264

422

299

1000

BMI

385

-326

621

-66

-24

387

1000

MxCc

233

248

307

168

906

384

116

1000

Comx

230

176

784

140

204

200

1000

ApBo

637

594

-37

169

332

608

319

1000

TvBo

485

654

-22

111

400

615

265

813

1000

Vcal

531

328

424

533

692

369

186

750

514

457

346

1000

VCt

566

280

446

403

651

386

255

729

446

502

372

928

1000

We found the strongest correlations (928) between CT Liver volumetry (VCt) and liver volume (calculated by formula) (Vcal) and the strongest negative correlation is -326 between BMI (BMI) and height (hgt).

Table 18 The characteristic square of a factor and the percentage contribution

sqare

sum

5.268

40.523

2.585

19.882

60.405

1.483

11.404

71.809

1.256

9.661

81.470

.841

6.468

87.938

.583

4.488

92.426

.433

3.331

95.757

.211

1.626

97.383

.142

1.095

98.478

.098

.751

99.229

.075

.574

99.804

.019

.148

99.952

.006

.048

100.000

Percentage representation of the characteristic squares fall in the range between .048% and 40.523%. The new structure is consisted of 4 isolated factors which contain 81.470 % information from the whole sample.

Table 19 Structure of 4 isolated factors for the anthropometric and linear hepatic measurements in the group of young examinees

Skkk

1 –

factor

2 –

factor

3 –

factor

4 –

factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

MxAp

641

640

410

373

139

-29

300

hgt

943

343

118

-280

-45

863

745

593

wgt

811

721

520

373

139

146

362

131

104

MxCo

914

305

-627

393

152

634

402

271

-161

MxCr

939

590

348

-469

220

-572

327

221

-210

D-il

377

569

324

117

-3

-200

BMI

843

490

240

646

417

161

211

-377

142

113

MxCc

920

729

531

101

-356

127

-484

234

158

-168

Comx

878

410

168

-529

280

108

655

429

289

-35

ApBo

785

717

514

264

102

-61

TvBo

752

665

443

541

292

113

126

-25

Vcal

925

882

779

148

-381

145

-10

-37

VCt

864

884

781

148

-276

-59

-54

13.0

1000

The factor structure for the anthropometric and linear hepatic measurements in the group of young examinees

* Decreased communality shows that the structure of 4 isolated factors does not contain enough information about 1 anthropometric and linear hepatic measurement: Diaphragm to iliac (D-il) 377.

The variables that contribute in forming the structure of each isolated factor are: height, Maximal Crainocaudal, liver volume (calculated by formula), Max CC, Maximal Coronal, Cormax LL, CT Liver volumetry, BMI, weight, AP body dimension, Transverse body dimension, Maximal Ap, the variable that does not not contribute to factor structure is: Diaphragm to iliac.

* Structure of the 1st- isolated factor is formed of 7 anthropometric and linear hepatic measurements: CT Liver volumetry (VCt) with factor contribution (cor) 782, liver volume (calculated by formula) (Vcal) 779, Max CC (MxCc) 531, weight (wgt) 520, AP body dimension (ApBo) 515, Transverse body dimension (TvBo) 443, Maximal Ap (MxAp) 411. Latent variables are: Maximal Crainocaudal (MxCr) 349, Diaphragm to iliac (D-il) 324. Association CT Liver volumetry is in concordance with: liver volume (calculated by formula), Max CC, weight, AP body dimension, Transverse body dimension, Maximal Ap, Maximal Crainocaudal, Diaphragm to iliac.

* Structure 4.- isolated factor is formed of 1 anthropometric and linear hepatic measurement: height (hgt) with factor contribution (cor) 746.

* Several factors contribute to variable for: Maximal Coronal, factor-2 (393), factor-3 (403), Maximal Crainocaudal, factor-1 (349), factor-3 (327), Cormax LL, factor-2 (280), factor-3 (429), Transverse body dimension, factor-1 (443), factor-2 (293).

In forming the structure of 4 isolated factors in the group of young examinees contribute all 13 (100.00%) anthropometric and linear hepatic measurements.

The concordance of anthropometric and linear hepatic measurements in the group of young examinees and structure of isolated factors

In forming the structure of 4 isolated factors 126 examinees (82.89%), have high contribution 15 (9.87%) examinees have intermediate contribution, low contribution without significance have 11 (7.24%) examinees.

3. – for 16 (10.53%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure of 3 isolated factor. Latently related to the structure are 13 (8.55%) examinees. For 13 examinees we found direct proportionality, and 16 are inversely related.

4. – for 6 (3.95%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure of 4 isolated factor. Latently related to the structure are 12 (7.89%) examinees. For 11 examinees we found direct proportionality, and 7 are inversely related.

Concordance of anthropometric and linear hepatic measurements with the structure: two and more factor have 2 examinees, with one factor have 102 examinees, latent agreement only have 32 examinees, with no agreement are 16 examinees.

It should be noted that 3 examinees stand out from the rest (inr)

Graph 6 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 7 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 8 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 9 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Table 20 Grouping of the age groups for the anthropometric and linear hepatic measurements

level

closeness

age groups-0,age groups-0

.10

age groups-0,age groups-0

.12

age groups-0,age groups-0

.15

18-47g,66-86g

.19

age groups-0,age groups-0

.20

18-47g,age groups-0

.22

18-47g,age groups-0

.41

48-65g,age groups-0

.46

48-65g,age groups-0

.74

48-65g,age groups-0

.95

48-65g,age groups-0

1.82

18-47g,48-65g

2.62

From the dendrogram shown we can see that the age groups-0 and age groups-0 are the closest with the distance .10.The biggest difference is between the group of young 18-47 and middle-aged 48-65, with the distance 2.62.

Legend: age 18-47 (1) age 48-65 (2) age 66-86 (3) ;;strG-0;; (4) ;;strG-0;; (5) ;;strG-0;; (6) ;;strG-0;; (7) ;;strG-0;; (8) strG-0 (9) strG-0;; (10) ;;strG-0;; (11) ;;strG-0;; (12) ;;strG-0;; (13)

Mutual contribution of the dividing classes and factor structure for anthropometric and linear hepatic measurements

Table 21 Contributions among dividing groups (3) and isolated factor structure for anthropometric and linear hepatic measurements examinees

Skkk

1-factor

2-factor

3-factor

4-factor

weight

inr

kvl

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

18-47g

171

1000

567

178

-1208

807

156

48-65g

461

1000

178

282

-84

-188

312

-197

343

66-86g

368

1000

-486

312

666

586

162

225

As shown in Table (21) the highest weight is 461 for the class (age 48-65). This means that the biggest part of the sample which belongs to one class, is exactly in that class to which the stated weighting factor corresponds, and the next is for the class: (age 66-86) (368.), and 18-47 (171.).

* Inertia (inr) of the class age 18-47 is 24, it means that this class stands out from the rest, and the next is for the class: old examinees (age 66-86) (21.) and age 48-65 (4.).

* Relative contribution (cor) 1. – of the axis to the class old examinees (age 66-86) is low 312. which means that the axis has the most information about that class, then for: middle-aged (age 48-65) (282.-low) and young (age 18-47) (178.-without significance). Relative contribution 2. – of the axis to the class (age 18-47) is 807. high, then for: (age 66-86) (586.-intermediate), (age 48-65) (63.-without significance). Relative contribution 3. – of the axis to the class (age 48-65) is 312. low, then for: (age 66-86) (35.-without significance), (age 18-47) (13.-without significance). Relative contribution 4. – of the axis to the class (age 48-65) is 343. low, then for: (age 66-86) (67.-without significance), (age 18-47 (1.-without significance).

* Relative contribution of the class (age 66-86) to inertia of the 1st – axis is 17., then for: (age 18-47 (10), (age 48-65 (3). Relative contribution of the class (age 18-47 to to inertia of the 2nd – axis is 97, then for: (age 66-86 (63.), (age 48-65 (1.). Relative contribution of the class (age 48-65 to inertia of the 3rd – axis is 11, then for: (age 66-86 (7.), (age 18-47 (3.). Relative contribution of the class (age 66-86) to inertia 4th – axis is 15, then for: (age 48-65 (14.), (age 18-47 (0.).

*, and inversely proportional for the classes of middle-aged (age 48-65) and young (age 18-47). Association of the class on the axis 3. – is proportional for the classes of old examinees (age 66-86) and middle-aged (age 18-47), and inversely proportional for the class of middle-aged examinees (age 48-65). Association of the class on the axis 4. – is proportional for the classes (age 66-86) and (age 18-47), and inversely proportional for the class (age 48-65).

Table 22 Contribution of the factor to a to a class in ‰

Age

18-47

178

807

48-65

282

312

343

66-86

312

586

* The highest contribution to the class of young examinees (age 18-47) is the factor F2 (807‰) then F1 (178‰) which contributess 4.5 times less. The highest contribution to the class (age 48-65) is the factor F3 (312 ‰) then factor F1 (282 ‰) which contributess 1.1 times less, then F4 (343 ‰) which contributess .9 times less. The highest contribution to a class (age 66-86) is the factor F2 (586 ‰) then F1 (312 ‰) which contributess 1.9 times less.

Table 23 Absolute contribution of the class and inertia of factor axis

Age

mass

dcnt

actr1

actr2

actr3

actr4

18-47

171

1807

249

48-65

461

112

66-86

368

757

163

* Distance between center of the class and the cloud center (dcnt) is the biggest for the class of young examinees (age 18-47) (1807), this means that this class stands out the most from the others followed by: the class of old examinees (age 66-86)(757) and the class of middle-aged (age 48-65)(112).

* Absolute contribution of the class old examinees (age 66-86) to inertia of the 1.- axis (86), followed by: class (age 18-47) (54), class (age 48-65)(14). Absolute contribution of the class (age 18-47) to inertia of the 2nd axis (249), followed by: class (age 66-86) (163) and class (age 48-65) (3). Absolute contribution of the class (age 48-65) to inertia of the 3rd axis (16), followed by: class (age 66-86) (9), class (age 18-47) (4). Absolute contribution of the class (age 66-86) to inertia of the 4th- axis (18), followed by: class (age 48-65) (17), class (age 18-47) (0). The greatest absolute contribution of the class (age 18-47) to axis inertia is for 2nd- axis (249) then for the 3rd- axis (4), 4th- axis (0). The highest absolute contribution of the class (age 48-65) inertia of the axis is for the 3rd- axis (16) then for the 2nd- axis (3), and the 4th- axis (17). The greatest absolute contribution of the class (age 66-86) to axis inertia is for the 2nd- axis (163) then for the 3rd- axis (9) and the 4th- axis (18).

Table 24 Mutual contributions of the isolated factors structures and diferences of two groups (dipoles)

Skkk

1-factor

2-factor

3-factor

4-factor

Group

inr

kvl

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

198

1000

-389

1124

794

-344

-242

544

1000

-1054

238

1874

755

159

180

267

1000

-665

339

750

431

350

422

136

Table 25 Mahalanobis distance between age groups for anthropometric and linear hepatic measurements

Age

18-47

48-65

66-86

18-47g

.00

.86

1.39

48-65g

.86

.00

.79

66-86g

1.39

.79

.00

By calculating Mahalanobis distance between groups we are obtaining another indicator of similarities or differences. Distances of different spaces can be compared. According to the results in the table 25 we can say that the distance is minimal between age groups for (age 66-86) and age 48-65 ((age 66-86) and (age 48-65) (.79) (intermediate) and the farthest are age groups: (age 66-86) and age 18-47 (age 66-86) and (age 18-47) (1.39) (bigger).

Table 26 Grouping of the age groups for anthropometric and linear hepatic measurements

level

closeness

48-65,66-86

.79

18-47,48-65

1.14

From the dendrogram shown it can be seen that the closest are groups (age 48-65) and (age 66-86) with the distance .79, and the biggest difference is between (age 18-47) and (age 48-65), distance 1.14.

Legend: age 18-47 (1) age 48-65 (2) (age 66-86) (3)

Analysis of the structure for age 48-65 (70) and (age 66-86) (56)

In accordance to the previously established design of the study, it was planned to extract optimal number of factors from the sample of 26 examinees, using factor analysis of principal components, from 13 anthropometric and linear hepatic measurements: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal), CT Liver volumetry (VCt). The aim is to find the associations between individual variables, to determine the contribution of each factor to a variable, to apply complementary analyses and to present the results graphically. The coordinates of the variables for anthropometric and linear hepatic measurements will be presented to determine their position in an isolated structure.

Structure of 4 isolated factor for anthropometric and linear hepatic measurements

Table 27 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

VCt

hgt

1000

wgt

598

1000

BMI

-19

785

1000

D-il

522

582

1000

ApBo

291

790

747

235

1000

TvBo

146

709

776

242

855

1000

MxAp

399

731

590

482

736

566

1000

MxCo

-114

-102

-35

-66

-61

-148

1000

MxCr

260

537

432

178

636

496

599

-177

1000

MxCc

266

571

483

300

636

524

669

-158

962

1000

Comx

137

-15

-98

781

-191

-139

1000

Vcal

308

662

558

319

729

596

792

292

785

797

217

1000

VCt

374

704

567

383

747

559

862

782

826

116

939

1000

We found the strongest correlations (962) between Max CC (MxCc) and Maximal Crainocaudal (MxCr) and The strongest negative correlation is -191 between Cormax LL (Comx) and Maximal Crainocaudal (MxCr).

Table 28 The characteristic square of a factor and the percentage contribution

sqare

sum

6.858

52.752

1.966

15.126

67.877

1.302

10.015

77.892

1.102

8.479

86.371

.877

6.747

93.118

.397

3.052

96.169

.179

1.373

97.542

.156

1.197

98.739

.084

.644

99.383

.044

.337

99.719

.032

.244

99.964

.004

.031

99.994

.001

.006

100.000

Percentage representation of the characteristic squares fall in the range between .006% and 52.752%. The new structure is consisted of 4 isolated factors which contain 86.371 % information of the whole sample.

Table 29 Structure of 4 isolated factors for anthropometric and linear hepatic measurements

Skkk

1 –

factor

2 –

factor

3 –

factor

4 –

factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

941

396

157

-383

147

113

795

632

573

wgt

936

874

765

111

-20

200

362

131

119

BMI

944

768

590

-92

570

325

250

-142

D-il

596

476

226

-113

531

282

217

273

ApBo

802

883

781

114

105

-99

TvBo

721

771

595

-55

293

-192

MxAp

791

872

761

111

-10

142

MxCo

932

-49

-935

873

444

-190

-141

MxCr

911

800

640

243

-373

139

107

-270

MxCc

885

838

703

102

197

-305

-224

Comx

892

-935

875

445

-37

127

Vcal

961

892

795

116

-261

-284

-133

VCt

916

918

843

123

-109

-246

-29

13.0

1000

The factor structure for anthropometric and linear hepatic measurements

* The communality is higher for: liver volume (calculated by formula) (Vcal) 961, BMI (BMI) 944, height (hgt) 941, weight (wgt) 936, Maximal Coronal (MxCo) 932, CT Liver volumetry (VCt) 916, Maximal Crainocaudal (MxCr) 911, Cormax LL (Comx) 892, Max CC (MxCc) 885, AP body dimension (ApBo) 802, Maximal Ap (MxAp) 791, Transverse body dimension (TvBo) 721.

* Intermediate communality shows that the structure of 4 isolated factors contain intermediate information about 1 anthropometric and linear hepatic measurement: Diaphragm to iliac (D-il) 596.

The variables that contribute in forming the structure of each isolated factor are: liver volume (calculated by formula), BMI, height, weight, Maximal Coronal, CT Liver volumetry, Maximal Crainocaudal, Cormax LL, Max CC, AP body dimension, Maximal Ap, Transverse body dimension, Diaphragm to iliac, the variables that do not contribute to factor structure are:

* Structure of the 1st- isolated factor is formed of 9 anthropometric and linear hepatic measurements: CT Liver volumetry (VCt) with factor contribution (cor) 843, liver volume (calculated by formula) (Vcal) 796, AP body dimension (ApBo) 781, weight (wgt) 765, Maximal Ap (MxAp) 761, Max CC (MxCc) 703, Maximal Crainocaudal (MxCr) 640, Transverse body dimension (TvBo) 596, BMI (BMI) 591. Association CT Liver volumetry is in concordance with: liver volume (calculated by formula), AP body dimension, weight, Maximal Ap, Max CC, Maximal Crainocaudal, Transverse body dimension, BMI.

* Structure of the 2nd- isolated factor is formed of 2 anthropometric and linear hepatic measurements: Cormax LL (Comx) with factor contribution (cor) 875, Maximal Coronal (MxCo) 874. Association of Cormax LL is in concordance with: Maximal Coronal.

* Structure of the 3rd- isolated factor is formed of 2 latent anthropometric and linear hepatic measurements: BMI (BMI) with factor contribution (cor) 326, Diaphragm to iliac (D-il) 283. Association BMI is in concordance with: Diaphragm to iliac.

* Structure 4.- isolated factor is formed of 1 anthropometric and linear hepatic measurement: height (hgt) with factor contribution (cor) 632.

* Several factors contribute to variable for: BMI, factor-1 (591), factor-3 (326).

In forming the structure of isolated factors contribute all 13 (100.00%) anthropometric and linear hepatic measurements.

Concordance of anthropometric and linear hepatic measurements and structures of isolated factors

In forming the structure of 4 isolated factors 23 examinees (88.46%) have high contribution, 2 examinees (7.69%) have intermediate contribution, 1 examinee (3.85%) is with low contribution without significance.

1. – for 12 (46.15%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 3 (11.54%) examinees. For 5 examinees we found direct proportionality, and for 10 examinees were inversely related.

2. – for 5 (19.23%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure are 4 (15.38%) examinees. For 5 examinees we found direct proportionality, and 4 examinees were inversely related.

3. – for 1 (3.85%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure is 1 (3.85%) examinee. For 2 examinees we found direct proportionality.

4. – for 3 (11.54%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 4 isolated factor. Latently related to the structure are 2 (7.69%) examinees. For 3 examinees we found direct proportionality, and 2 examinees were inversely related.

Concordance of anthropometric and linear hepatic measurements with the structure: one factor have 21 examinees, latent agreement only have 3 examinees, with no agreement are 2 examinees.

It should be noted that 1 examinee stands out from the rest (inr)

Graph 10 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structures

Graph 11 Graphicalal representation of anthropometric and linear hepatic measurements in the isolated factors structures 1F and 2F

Graph 12 Graphicalal representation of anthropometric and linear hepatic measurements in the isolated factors structures 1F and 3F

Graph 13 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structures 2F and 3F

Analysis of the structure (age 66-86) (56)

In accordance to the previously established design of the study, it was planned to extract optimal number of factors using principal components analysis from the data set consisted of 13 anthropometric and linear hepatic measurements in 70 examinees. Anthropometric and linear hepatic measurements are :height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal), CT Liver volumetry (VCt). The aim is to find the associations between individual variables, to determine the contribution of each factor to a variable, to apply complementary analyses and to present the results Graphically. The coordinates of the variables for anthropometric and linear hepatic measurements will be presented to determine their position in an isolated structure.

Table 30 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

VCt

hgt

1000

wgt

400

1000

BMI

-468

593

1000

D-il

-113

427

492

1000

ApBo

-59

559

584

408

1000

TvBo

-23

614

576

500

859

1000

MxAp

139

492

412

307

658

555

1000

MxCo

141

-106 exam

1000

MxCr

218

106

-53

144

103

-16

-27

1000

MxCc

245

272

253

290

305

236

854

1000

Comx

210

115

158

788

-79

1000

Vcal

267

470

266

302

552

445

592

504

530

675

454

1000

VCt

150

436

341

337

581

466

566

455

499

648

442

935

1000

We found the strongest correlations (935) between CT Liver volumetry (VCt) and liver volume (calculated by formula) (Vcal). The strongest negative correlation is -468 between BMI (BMI) and height (hgt).

Table 31 The characteristic square of a factor and the percentage contribution

sqare

sum

5.182

39.862

2.322

17.858

57.719

1.874

14.418

72.137

1.241

9.548

81.685

.817

6.283

87.969

.538

4.135

92.104

.478

3.679

95.783

.220

1.696

97.479

.129

.996

98.475

.102

.783

99.258

.074

.571

99.829

.016

.122

99.950

.006

.050

100.000

Percentage representation of the characteristic squares fall in the range between .050% and 39.862%. The new structure is consisted of 4 isolated factors which contain 81.685 % information from the whole data set.

Table 32 Structure of 4 isolated factors for the anthropometric and linear hepatic measurements

Skkk

1 –

factor

2 –

factor

3 –

factor

4 –

factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

947

155

534

286

123

-159

782

612

493

wgt

735

722

522

101

-188

421

177

143

BMI

817

583

340

-616

380

164

131

-283

D-il

458

551

304

-325

105

-72

-208

ApBo

787

802

643

124

-375

141

TvBo

773

760

578

111

-426

182

-85

MxAp

671

688

474

-275

-96

335

112

MxCo

908

314

454

206

766

586

313

-130

MxCr

925

402

161

565

320

138

-578

335

179

-331

109

MxCc

915

616

380

472

223

-505

255

136

-240

Comx

867

361

130

330

109

791

626

334

-34

Vcal

929

875

765

148

398

159

-39

VCt

887

873

763

147

317

101

-138

13.0

1000

The factor structure anthropometric and linear hepatic measurements

* The communality is higher for: height (hgt) 947, liver volume (calculated by formula) (Vcal) 929, Maximal Crainocaudal (MxCr) 925, Max CC (MxCc) 915, Maximal Coronal (MxCo) 908, CT Liver volumetry (VCt) 887, Cormax LL (Comx) 867, BMI (BMI) 817, AP body dimension (ApBo) 787, Transverse body dimension (TvBo) 773, weight (wgt) 735, Maximal Ap (MxAp) 671.

* Intermediate communality shows that the structure of 4 isolated factors contain intermediate information about 1 anthropometric and linear hepatic measurement: Diaphragm to iliac (D-il) 458.

The variables that contribute in forming the structure of each isolated factor are: height, liver volume (calculated by formula), Maximal Crainocaudal, Max CC, Maximal Coronal, CT Liver volumetry, Cormax LL, BMI, AP body dimension, Transverse body dimension, weight, Maximal Ap, Diaphragm to iliac, the variables that do not contribute to factor structure are:

* Structure of the 1st- isolated factor is formed of 6 anthropometric and linear hepatic measurements: liver volume (calculated by formula) (Vcal) with factor contribution (cor) 766, CT Liver volumetry (VCt) 763, AP body dimension (ApBo) 643, Transverse body dimension (TvBo) 578, weight (wgt) 522, Maximal Ap (MxAp) 474. Latent variables are: Max CC (MxCc) 380, BMI (BMI) 340, Diaphragm to iliac (D-il) 304. Association of the liver volume (calculated by formula) is in concordance with: CT Liver volumetry, AP body dimension, Transverse body dimension, weight, Maximal Ap, Max CC, BMI, Diaphragm to iliac.

* Structure of the 2nd- isolated factor is formed of 3 latent anthropometric and linear hepatic measurements: BMI (BMI) with factor contribution (cor) 380, Maximal Crainocaudal (MxCr) 320, height (hgt) 286. Association BMI is inversely proportional with: Maximal Crainocaudal, height.

* Structure of the 3rd- isolated factor is formed of 2 anthropometric and linear hepatic measurements: Cormax LL (Comx) with factor contribution (cor) 627, Maximal Coronal (MxCo) 587. Latent variables are: Maximal Crainocaudal (MxCr) 335. Association Cormax LL is in concordance with: Maximal Coronal. Association Cormax LL is inversely proportional with: Maximal Crainocaudal.

* Structure 4.- isolated factor is formed of 1 anthropometric and linear hepatic measurement: height (hgt) with factor contribution (cor) 612.

* Several factors contribute to variable for: height, factor-2 (286), factor-4 (612), BMI, factor-1 (340), factor-2 (380), Maximal Crainocaudal, factor-2 (320), factor-3 (335).

In forming the structures of isolated factors contribute all 13 (100.00%) anthropometric and linear hepatic measurements.

Concordance of anthropometric and linear hepatic measurements and structures of isolated factors

In forming the structure of 4 isolated factors from the sample of 70 examinees we found that 59 examinees (84.29%) have high contribution, 6 examinees have (8.57%) intermediate contribution, with low contribution, without significance are 5 examinees (7.14%).

1. – for 28 (40.00%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 8 (11.43%) examinees. For 18 examinees we found direct proportionality, and 18 examinees were inversely related.

2. – for 10 (14.29%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure are 5 (7.14%) examinees. For 7 examinees we found direct proportionality, and 8 examinees were inversely related.

3. – for 8 (11.43%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure are 7 (10.00%) examinees. For 8 examinees we found direct proportionality, and for 7 examinees values are inversely related.

4. – for 4 (5.71%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 4 isolated factor. Latently related to the structure are 4 (5.71%) examinees. For 6 examinees we found direct proportionality, and 2 examinees were inversely related.

Concordance of anthropometric and linear hepatic measurements with the structure: two and more factor have 1 examinee, one factor have 48 examinees, latent agreement only have 11 examinees, with no agreement are 10 examinees.

It should be noted that 1 examinee stands out from the rest (inr)

Graph 14 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structures

Graph 15 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structures 1F and 2F

Graph 16 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structures 1F and 3F

Graph 17 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structures 2F and 3F

Analysis of the structure for the anthropometric and linear hepatic measurements

In accordance to the previously established design of the study, it was planned to extract optimal number of factors using principal components analysis from the data set consisted of 13 anthropometric and linear hepatic measurements in 56 examinees. Anthropometric and linear hepatic measurements are: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal), CT Liver volumetry (VCt). The aim is to find the associations between individual variables, to determine the contribution of each factor to a variable, contribution of each variable to a factor, to apply complementary analyses and to present the results Graphically. The coordinates of the variables for anthropometric and linear hepatic measurements will be presented to determine their position in an isolated structure.

Table 33 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

VCt

hgt

1000

wgt

664

1000

BMI

-64

699

1000

D-il

243

416

313

1000

ApBo

144

553

584

495

1000

TvBo

324

718

651

457

691

1000

MxAp

509

513

200

334

516

310

1000

MxCo

136

-46

-195

-101

-13

-26

1000

MxCr

-4

-135

316

247

155

269

1000

MxCc

178

239

416

398

194

265

273

899

1000

Comx

366

215

-66

193

196

224

732

316

411

1000

Vcal

358

266

-24

349

188

559

620

753

760

649

1000

VCt

346

328

376

396

236

589

451

723

754

559

917

1000

We found the strongest correlations (917) between CT Liver volumetry (VCt) and liver volume (calculated by formula) (Vcal) and the strongest negative correlation is -195 between Maximal Coronal (MxCo) and BMI (BMI).

Table 34 The characteristic square of a factor and the percentage contribution

sqare

sum

5.292

40.705

2.923

22.486

63.192

1.466

11.276

74.467

1.081

8.319

82.786

.689

5.299

88.085

.572

4.401

92.486

.386

2.967

95.453

.241

1.856

97.309

.187

1.435

98.744

.094

.725

99.469

.061

.470

99.939

.007

.052

99.991

.001

.009

100.000

Percentage representation of the characteristic squares fall in the range between .009% and 40.705%. The new structure is consisted of 4 isolated factors which contain 82.786 % information o the whole sample.

Table 35 Structure of 4 isolated factors for anthropometric and linear hepatic measurements

Skkk

1 –

factor

2 –

factor

3 –

factor

4 –

factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

857

517

267

125

-645

417

284

397

158

146

wgt

887

632

400

633

400

137

-294

BMI

848

320

102

751

564

193

181

-386

149

138

D-il

475

594

352

264

229

ApBo

765

642

412

512

262

295

-57

TvBo

811

558

312

635

404

138

-50

-305

MxAp

759

648

420

220

-198

501

251

232

MxCo

907

384

147

-599

359

123

-369

137

-514

264

245

MxCr

911

636

404

-499

249

495

245

167

112

MxCc

870

769

591

112

-317

100

422

178

122

Comx

849

603

363

-405

164

-429

184

126

-371

138

127

Vcal

947

871

758

143

-433

187

-6

VCt

878

873

762

144

-316

100

104

13.0

1000

The structures of isolated factors for anthropometric and linear hepatic measurements

* The communality is higher for: liver volume (calculated by formula) (Vcal) 947, Maximal Crainocaudal (MxCr) 911, Maximal Coronal (MxCo) 907, weight (wgt) 887, CT Liver volumetry (VCt) 878, Max CC (MxCc) 870, height (hgt) 857, Cormax LL (Comx) 849, BMI (BMI) 848, Transverse body dimension (TvBo) 811, AP body dimension (ApBo) 765, Maximal Ap (MxAp) 759.

* Intermediate communality shows that the structure of 4 isolated factors contain intermediate information about 1 anthropometric and linear hepatic measurement: Diaphragm to iliac (D-il) 475.

The variables that contribute in forming the structure of each isolated factor are: liver volume (calculated by formula), Maximal Crainocaudal, Maximal Coronal, weight, CT Liver volumetry, Max CC, height, Cormax LL, BMI, Transverse body dimension, AP body dimension, Maximal Ap, Diaphragm to iliac, the variables that do not contribute to factor structure are:

* Structure of the 1st- isolated factor is formed of 7 anthropometric and linear hepatic measurements: CT Liver volumetry (VCt) with factor contribution (cor) 763, liver volume (calculated by formula) (Vcal) 759, Max CC (MxCc) 591, Maximal Ap (MxAp) 421, AP body dimension (ApBo) 413, Maximal Crainocaudal (MxCr) 405, weight (wgt) 400. Latent variables are: Cormax LL (Comx) 364, Diaphragm to iliac (D-il) 353, Transverse body dimension (TvBo) 312. Association of the CT Liver volumetry is in concordance with: liver volume (calculated by formula), Max CC, Maximal Ap, AP body dimension, Maximal Crainocaudal, weight, Cormax LL, Diaphragm to iliac, Transverse body dimension.

* Structure of the 2nd- isolated factor is formed of 3 anthropometric and linear hepatic measurements: BMI (BMI) with factor contribution (cor) 564, Transverse body dimension (TvBo) 404, weight (wgt) 401. Latent variables are: Maximal Coronal (MxCo) 359. Association BMI is in concordance with: Transverse body dimension, weight. Association BMI is inversely proportional with: Maximal Coronal.

* Structure of the 3rd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: height (hgt) with factor contribution (cor) 417.

* Structure 4.- isolated factor is not possible to define.

* Several factors contribute to variable for: weight, factor-1 (400), factor-2 (401), Transverse body dimension, factor-1 (312) and factor-2 (404).

In forming the structure of two and more factors 2 anthropometric and linear hepatic measurements contribute the most. In forming the structure of isolated factors contribute all 13 (100.00%) anthropometric and linear hepatic measurements.

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

We found that in forming the structure of 4 isolated factors from the sample of 56 examinees, 46 examinees (82.14%) have high contribution, 5 examinees (8.93%) have intermediate contribution, with low contribution without significance are 5 examinees (8.93%).

1. – for 17 (30.36%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 5 (8.93%) examinees. For 7 examinees we found direct proportionality, and 15 examinees were inversely related.

2. – for 13 (23.21%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factors. Latently related to the structure are 5 (8.93%) examinees. For 9 examinees we found direct proportionality, and 9 examinees were inversely related.

3. – for 7 (12.50%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factors. Latently related to the structure are 4 (7.14%) examinees. For 6 examinees we found direct proportionality, and 5 examinees were inversely related.

4. – for 4 (7.14%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 4 isolated factors. Latently related to the structure are 1 (1.79%) examinee, and 4 examinees were inversely related.

Concordance of the anthropometric and linear hepatic measurements with the structure: one factor have 41 examinees, latent agreement only have 7 examinees, with no agreement are 8 examinees.

It should be noted that 1 examinee stands out from the rest (inr)

Graph 18 Graphicalal representation of the anthropometric and linear hepatic measurements in isolated factor structures

Graph 19 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structures 1F and 2F

Graph 20 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structures 1F and 3F

Graph 21 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structures 2F and 3F

SAMPLE 550

THE FACTOR Structure FOR AGE

Analysis of the structure of the anthropometric and linear hepatic measurements

In accordance to the previously established design of the study, it was planned to extract optimal number of factors using principal components analysis from the dataset consisted of 12 anthropometric and linear hepatic measurements of 50 examinees. Anthropometric and linear hepatic measurementsare: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal). The aim is to find the associations between individual variables, to determine the contribution of each factor to a variable, contribution of each variable to a factor, to apply complementary analyses and to present the results graphically. The coordinates of the variables for anthropometric and linear hepatic measurements will be presented to determine their position in an isolated structure.

Structure of 3 isolated factors for the anthropometric and linear hepatic measurements

In this chapter we analysed the structure of 3 isolated factors (Principal Component Analysis) from 12 anthropometric and linear hepatic measurements: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal), on a sample of 50 individuals.

Table 1 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

515

1000

BMI

891

1000

D-il

378

503

386

1000

ApBo

271

695

662

386

1000

TvBo

303

818

791

445

816

1000

MxAp

225

636

620

457

659

623

1000

MxCo

135

-71

-34

-79

1000

MxCr

264

388

300

173

384

287

447

1000

MxCc

285

469

388

291

472

382

591

949

1000

Comx

195

-29

-10

-54

-133

916

1000

Vcal

303

523

443

240

469

482

616

614

709

751

541

1000

We found the strongest correlations (949) between Max CC (MxCc) and Maximal Crainocaudal (MxCr) and the strongest negative correlation is -133 between Cormax LL (Comx) and Maximal Ap (MxAp).

Table 2 The characteristic square of a factor and the percentage contribution

sqare

sum

5.530

46.083

2.326

19.380

65.463

1.455

12.129

77.592

1.046

8.714

86.306

.610

5.087

91.393

.427

3.561

94.954

.355

2.961

97.915

.129

1.076

98.991

.083

.688

99.679

.032

.263

99.942

.005

.042

99.984

.002

.016

100.000

Percentage representation of the characteristic squares fall in the range between .016% and 46.083%. The new structure is consisted of 3 isolated factors which contain 77.592 % information of the whole sample.

Table 3 Structure of 3 isolated factors for the anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

239

451

204

145

-121

wgt

884

880

775

140

-155

-291

BMI

760

783

613

111

-257

-285

D-il

393

545

297

-214

-225

ApBo

723

802

643

116

-245

-141

TvBo

849

829

687

124

-166

-367

134

MxAp

708

802

643

116

-235

102

MxCo

950

172

925

856

368

-255

MxCr

938

659

435

167

689

475

327

MxCc

966

751

565

102

106

625

390

268

Comx

949

149

915

837

360

-300

Vcal

952

786

618

112

542

294

126

198

12.0

1000

The factor structure anthropometric and linear hepatic measurements

Whole sample that consisted of 12 anthropometric and linear hepatic measurements was reduced to 3 isolated factors. Contribution of isolated factor (qlt) is significant for 10 anthropometric and linear hepatic measurements.

* The communality is higher for: Max CC (MxCc) 966, liver volume (calculated by formula) (Vcal) 952, Maximal Coronal (MxCo) 950, Cormax LL (Comx) 949, Maximal Crainocaudal (MxCr) 938, weight (wgt) 884, Transverse body dimension (TvBo) 849, BMI (BMI) 760, AP body dimension (ApBo) 723, Maximal Ap (MxAp) 708.

* Decreased communality shows that the structure of 3 isolated factors does not contain enough information about 2 anthropometric and linear hepatic measurements: Diaphragm to iliac (D-il) 393, height (hgt) 239.

The variables that contribute in forming the structure of each isolated factor are: Max CC, liver volume (calculated by formula), Maximal Coronal, Cormax LL, Maximal Crainocaudal, weight, Transverse body dimension, BMI, AP body dimension, Maximal Ap, the variables that do not contribute to factor structure are: Diaphragm to iliac, height.

* Structure of the 1st- isolated factor is formed of 8 anthropometric and linear hepatic measurements: weight (wgt) with factor contribution (cor) 776, Transverse body dimension (TvBo) 687, AP body dimension (ApBo) 643, Maximal Ap (MxAp) 643, liver volume (calculated by formula) (Vcal) 619, BMI (BMI) 613, Max CC (MxCc) 565, Maximal Crainocaudal (MxCr) 435. Latent variables are: Diaphragm to iliac (D-il) 297. Weighting is in concordance with: Transverse body dimension, AP body dimension, Maximal Ap, liver volume (calculated by formula), BMI, Max CC, Maximal Crainocaudal, Diaphragm to iliac.

* Structure of the 2nd- isolated factor is formed of 2 anthropometric and linear hepatic measurements: Maximal Coronal (MxCo) with factor contribution (cor) 856, Cormax LL (Comx) 837. Latent variables are: liver volume (calculated by formula) (Vcal) 294. Association Maximal Coronal is in concordance with: Cormax LL, liver volume (calculated by formula).

* Structure of the 3rd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: Maximal Crainocaudal (MxCr) with factor contribution (cor) 476. Latent variables are: Max CC (MxCc) 391. Association Maximal Crainocaudal is in concordance with: Max CC.

* Several factors contribute to variable for: Maximal Crainocaudal, factor-1 (435), factor-3 (476), Max CC, factor-1 (565), factor-3 (391), liver volume (calculated by formula), factor-1 (619), factor-2 (294).

In forming the structure of two and more factors contribute 3 anthropometric and linear hepatic measurements, in forming only one factor contribute 8 anthropometric and linear hepatic measurements, with low contribution without significance in forming the factor is 1 anthropometric and linear hepatic measurement. In forming the structure of isolated factors contribute 11 (91.67%) anthropometric and linear hepatic measurements.

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

Analysis of the sample consisting of 50 examinees revealed that in forming the structure of 3 isolated factors 33 (66.00%) have high contribution, 12 (24.00%) have intermediate contribution and 5 (10.00%) are with low contribution, without significance.

1. – for 17 (34.00%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 4 (8.00%) examinees. For 8 examinees we found direct proportionality, and 13 were inversely related.

2. – for 11 (22.00%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure are 4 (8.00%) examinees. For 7 examinees we found direct proportionality, and 8 were inversely related.

3. – for 5 (10.00%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure are 4 (8.00%). For 5 examinees we found direct proportionality, and 4 were inversely related.

Concordance of anthropometric and linear hepatic measurements with the structure: two and more factor have 1 examinee, one factor have 31 examinees, latent agreement only have 7 examinees, with no agreement are 11 examinees.

It should be noted that 1 examinee stands out from the rest (inr)

Cluster analysis based on the isolated factors for the anthropometric and linear hepatic measurements

In this part of the study we clusterised 50 examinees based on 3 isolated factors from 12 variables ( anthropometric and linear hepatic measurements).

Suma nivoa mera 1.159

Table 5 Cluster grouping based on the isolated factors for the anthropometric and linear hepatic measurements

class

distance

class1

class2

nbr.elemn.

465

194

111

Group-1 (knot 94) that contains of 16 examinees, is consisted of sublevels, knots 90 and 86, the distance between them is 48. Group-2 (knot 96) contains 13 examinees is consisted of sublevels, knots 91 and 95 the distance between them is 87. Group-3 (knot 97) that contains 21 examinees, is consisted of sublevels, knots 93 and 83 the distance between them is 112.

Mutual contributions of the hierarchical classification classes and the isolated factors structures for the anthropometric and linear hepatic measurements

In this part of the study we analysed 11 upper classes of the hierarchical classification and 3 isolated classeses from the sample consisting of 50 examinees in relation to the 3 isolated factors structures for the anthropometric and linear hepatic measurements. The isolated classes are: 94, 96, 97.

Centers of hierarchical classification classes and isolated factors

Table 6 Centers of 3 hierarchical classification classes in relation to 3 isolated factors structures

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qlt

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

1000

903

740

624

-146

-718

164

198

420

422

222

1037

-1257

131

285

-142

260

318

317

416

2043

284

467

-562

140

204

571

2343

314

139

2048

240

253

-547

320

218

403

-1699

353

167

-10

643

380

263

250

460

-1339

216

293

-267

100

114

487

2239

366

-1230

110

-388

120

122

644

-1832

276

2038

341

214

-581

160

175

700

-2985

677

258

-275

470

280

152

305

-176

-1378

292

229

-223

As shown in Table 6 the highest weight is 420 for isolated class-97. This means that the biggest part of the sample which belongs to one class, belongs to this class (that corresponds to the specified weighting factor), it is followed by: class-94 (320.), class-96 (260.).

* Inertia is 903 for class-99. This means that it stands out most prominently, it is followed by: class-98 (624.), class-97 (422.), class-96 (318.), class-93 (263.), class-94 (218.), class-95 (204.), class-90 (175.), class-89 (152.), class-91 (122.), class-92 (114.).

* Contribution of isolated factors 700. is high, for class-90 this means that isolated factors give the most information to this class, then for: class-91 (644.-high), class-95 (571.-intermediate), class-92 (487.-intermediate), class-94 (403.-intermediate), class-96 (317.-low), class-89 (305.-low), class-93 (250.-without significance), class-97 (222.-without significance), class-98 (57.-without significance), class-99 (0.-without significance).

* Relative contribution of the 1st-isolated factor to the center of the class-90 is 677. high, this means that factor gives the most information to this class, then for: center of the class-92 (366.-low), center of the class-94 (353.-low), center of the class-95 (314.-low), center of the class-91 (276.-low), center of the class-97 (89.-without significance), center of the class-93 (25.-without significance), center of the class-96 (12.-without significance), center of the class-89 (5.-without significance), center of the class-98 (2.-without significance), center of the class-99 (0.-without significance). Relative contribution of the 2nd-isolated factor to the center of the class-91 is 341. low, then for: center of the class-89 (292.-low), center of the class-96 (284.-low), center of the class-95 (240.-without significance), center of the class-93 (216.-without significance), center of the class-97 (131.-without significance), center of the class-92 (110.-without significance), center of the class-98 (51.-without significance), center of the class-90 (6.-without significance), center of the class-99 (0.-without significance), center of the class-94 (0.-without significance). Relative contribution of the 3rd-isolated factor to the center of the class-94 is 50. without significance, then for: center of the class-91 (28.-without significance), center of the class-96 (22.-without significance), center of the class-95 (17.-without significance), center of the class-90 (17.-without significance), center of the class-92 (11.-without significance), center of the class-93 (9.-without significance), center of the class-89 (8.-without significance), center of the class-98 (4.-without significance), center of the class-97 (2.-without significance), center of the class-99 (0.-without significance).

* Association of the cluster for the 1st- factors structure is proportional between: class-99, class-94, class-98, class-97, class-99, inversely proportional with, class-97, class-96, class-95, class-93, class-92.

* Association of the cluster for the 2nd- factors structure is proportional between class-99, class-97, class-92, class-93, class-89, class-97, class-99, inversely proportional with: class-96, class-95, class-91.

* Association of the cluster for the 3rd- factors structure is proportional between: class-99, class-94, class-97, inversely proportional with: class-97, class-96, class-95, class-93, class-92, class-91, class-89.

Table 7 Center of hierarchical classification classes in relation to the factors axis 1 (factor variance: 5.5300)

knot

knot1

knot2

weight

inr

dst

(F1)2

acor

cor

ctr

cos

+cos2

1000

903

10841

740

624

10117

-146

-46

420

422

12048

1037

1076

452

299

260

318

14693

416

173

109

140

204

17468

2343

5489

768

314

139

561

314

320

218

8188

-1699

2887

924

353

167

-594

353

380

263

8310

460

211

160

100

114

13712

2239

5012

501

366

605

366

120

122

12183

-1832

3358

403

276

-525

276

160

175

13152

-2985

8907

1425

677

258

-823

677

280

152

6501

-176

-69

As shown in Table 7 the greatest distance (dst) 17468. is between the center of the cloud and the center of the class-95, it is followed by: class-96 (14693.), class-92 (13712.), class-90 (13152.), class-91 (12183.), class-97 (12048.), class-99 (10841.), class-98 (10117.), class-93 (8310.), class-94 (8188.), class-89 (6501.).

* Absolute contribution (acor) 1425. class-90 followed by absolute contribution for: class-94 (924.), class-95 (768.), class-92 (501.), class-97 (452.), class-91 (403.), class-93 (80.), class-96 (45.), class-98 (16.), class-89 (9.), class-99 (0.).

* The cosine of an angle (cos) -823. between the radius of the center of the class -90 and the axis, class-92 (605.), class-94 (-594.), class-95 (561.), class-91 (-525.), class-97 (299.), class-93 (160.), class-96 (109.), class-89 (-69.), class-98 (-46.), class-99 (0.).

Table 8 Center of hierarchical classification classes in relation to the factors axis 2 (factor variance: 2.3256)

knot

knot1

knot2

weight

inr

dst

(F2)2

acor

cor

ctr

cos

+cos2

1000

903

10841

740

624

10117

-718

515

381

164

-226

420

422

12048

-1257

1580

664

131

285

-362

220

260

318

14693

2043

4175

1086

284

467

533

296

140

204

17468

2048

4195

587

240

253

490

554

320

218

8188

-10

-4

353

380

263

8310

-1339

1793

681

216

293

-465

241

100

114

13712

-1230

1512

151

110

-332

476

120

122

12183

2038

4152

498

341

214

584

616

160

175

13152

-275

-76

683

280

152

6501

-1378

1900

532

292

229

-541

297

* Absolute contribution (acor) 1086. class-96 followed by absolute contribution for: class-93 (681.), class-97 (664.), class-95 (587.), class-89 (532.), class-91 (498.), class-98 (381.), class-92 (151.), class-90 (12.), class-99 (0.), class-94 (0.).

* The cosine of an angle (cos) 584. between the radius of the center of the class -91 and axis, class-89 (-541.), class-96 (533.), class-95 (490.), class-93 (-465.), class-97 (-362.), class-92 (-332.), class-98 (-226.), class-90 (-76.), class-94 (-4.), class-99 (0.).

Table 9 Center of hierarchical classification classes in relation to the factors axis 3 (factor variance: 1.4554)

knot

knot1

knot2

weight

inr

dst

(F3)2

acor

cor

ctr

cos

+cos2

1000

903

10841

740

624

10117

198

420

422

12048

-142

-41

222

260

318

14693

-562

316

-147

317

140

204

17468

-547

299

-131

571

320

218

8188

643

413

132

225

403

380

263

8310

-267

-93

250

100

114

13712

-388

151

-105

487

120

122

12183

-581

337

-166

644

160

175

13152

470

221

130

700

280

152

6501

-223

-88

305

* Absolute contribution (acor) 132. class-94, followed by absolute contribution for: class-96 (82.), class-95 (42.), class-91 (40.), class-90 (35.), class-98 (29.), class-93 (27.), class-92 (15.), class-89 (14.), class-97 (8.), class-99 (0.).

* The cosine of an angle (cos) 225. between the radius of the center of the class -94 and axis, class-91 (-166.), class-96 (-147.), class-95 (-131.), class-90 (130.), class-92 (-105.), class-93 (-93.), class-89 (-88.), class-98 (62.), class-97 (-41.), class-99 (0.).

Analysis of differences between two nodes (dipoles) of hierarchical classification classes

Table 10 Dipoles of the 11 highest nodes in relation to the factors axes from 1 to 3

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qld

cod

ctd

cod

ctd

cod

ctd

1000

3522

-562

131

-2761

3153

631

760

239

740

9038

-2736

7007

246

1247

1455

121

784

576

420

12724

-6062

11924

241

-861

241

-1313

560

260

12899

-4175

12898

204

-10

-34

140

3263

-288

-2723

3176

-345

320

11672

-2571

11006

-530

467

-346

199

380

12811

-2414

12704

-149

165

100

4424

-506

144

2364

3150

1416

1130

120

6272

-1851

4089

-1350

2175

-75

160

4821

187

-1195

3166

-844

1578

280

7776

1090

5756

-603

1764

-230

257

As shown in Table 10 we found that Inertia of the dipole (ind) a(n) b(n) is 39, class-99, followed by dipoles: class-98 (16.), class-97 (9.), class-96 (7.), class-95 (6.), class-94 (4.), class-93 (3.), class-92 (2.), class-91 (2.), class-90 (1.), class-89 (1.).

* The quality of the observed factors (qld) 12899. is high, for class-96 (dipole) which represents the quality of the vector ab representation in the factors space of this research, the other qualities are for: class-93 (12811.-high), class-97 (12724.-high), class-94 (11672.-high), class-98 (9038.-high), class-89 (7776.-high), class-91 (6272.-high), class-90 (4821.-high), class-92 (4424.-high), class-99 (3522.-high), class-95 (3263.-high).

* Projection ab on the axis

1st-isolated factor, that is, the projection of the dipole class-97 is -6062, other dipole projections on the axis are: class-96 (-4175.), class-98 (-2736.), class-94 (-2571.), class-93 (-2414.), class-91 (-1851.), class-89 (1090.), class-99 (-562.), class-92 (-506.), class-95 (-288.), class-90 (187.). Projection ab on the axis 2nd-isolated factor, that is, the projection of the dipole class-99 is -2761, other dipole projections on the axis are: class-95 (-2723.), class-92 (2364.), class-91 (-1350.), class-98 (1247.), class-90 (-1195.), class-97 (-861.), class-89 (-603.), class-94 (-530.), class-93 (-149.), class-96 (-10.). Projection ab on the axis 3rd-isolated factor, that is, the projection of the dipole class-92 is 1416, other dipole projections on the axis are: class-97 (-1313.), class-90 (-844.), class-98 (784.), class-99 (760.), class-94 (-346.), class-95 (-345.), class-89 (-230.), class-93 (165.), class-91 (-75.), class-96 (-34.).

* Relative contribution of the 1st-factors axis (D1), dipole a(n) b(n) is class-96 12898. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-93 (12704.-high), class-97 (11924.-high), class-94 (11006.-high), class-98 (7007.-high), class-89 (5756.-high), class-91 (4089.-high), class-92 (144.-without significance), class-99 (131.-without significance), class-90 (78.-without significance), class-95 (36.-without significance). Relative contribution of the 2nd-factors axis (D2), dipole a(n) b(n) is class-95 is 3176. (high), which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-90 (3166.-high), class-99 (3153.-high), class-92 (3150.-high), class-91 (2175.-high), class-89 (1764.-high), class-98 (1455.-high), class-94 (467.-intermediate), class-97 (241.-without significance), class-93 (48.-without significance), class-96 (0.-without significance). Relative contribution of the 3rd-factor axis (D3), dipole a(n) b(n) is class-90 is 1578. (high), which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-92 (1130.-high), class-98 (576.-intermediate), class-97 (560.-intermediate), class-89 (257.-without significance), class-99 (239.-without significance), class-94 (199.-without significance), class-93 (59.-without significance), class-95 (51.-without significance), class-91 (7.-without significance), class-96 (1.-without significance).

* Relative contribution of dipoles (ctd) of the class-98 to the 1st-factor axis is 7007, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-97 (11924.), class-96 (12898.), class-94 (11006.), class-93 (12704.), class-91 (4089.), class-89 (5756.), class-99 (131.), class-92 (144.), class-95 (36.), class-90 (78.). Relative contribution of dipoles (ctd) class-99 to the axis 2.-factor is 3153, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-98 (1455.), class-95 (3176.), class-92 (3150.), class-90 (3166.), class-91 (2175.), class-97 (241.), class-89 (1764.), class-94 (467.), class-93 (48.), class-96 (0.). Relative contribution of dipoles (ctd) class-98 to the axis 3.-factor is 576, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-99 (239.), class-97 (560.), class-92 (1130.), class-90 (1578.), class-94 (199.), class-89 (257.), class-95 (51.), class-93 (59.), class-96 (1.), class-91 (7.).

Table 11 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 1

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

192

465

-562

316

131

-361

131

182

262

-2736

7487

1360

7007

246

-2647

7007

266

-6062

36753

1330

11924

241

-3453

11924

336

-4175

17432

1126

12898

204

-3591

12898

476

-288

-189

150

-2571

6610

529

11006

-3317

11006

-2414

5829

430

12704

-3564

12704

284

-506

256

144

-380

144

186

-1851

3427

4089

-2022

4089

106

187

279

1090

1187

5756

2399

5756

As shown in Table 11 the greatest distance (dst) 476. between the center of the cloud and the center of the class is -95, it is followed by: class-99 (465.), class-96 (336.), class-92 (284.), class-97 (266.), class-98 (262.), class-91 (186.), class-94 (150.), class-90 (106.), class-93 (89.), class-89 (52.).

* Absolute contribution (acor) 1360. class-98, followed by absolute contribution for: class-97 (1330.), class-96 (1126.), class-94 (529.), class-93 (430.), class-91 (91.), class-89 (83.), class-99 (61.), class-92 (4.), class-95 (2.), class-90 (1.).

* The cosine of an angle (cos) -3591. between the radius of the center of the class -96 and axis, class-93 (-3564.), class-97 (-3453.), class-94 (-3317.), class-98 (-2647.), class-89 (2399.), class-91 (-2022.), class-92 (-380.), class-99 (-361.), class-90 (279.), class-95 (-189.).

Table 12 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 2

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

192

465

-2761

7624

1467

3153

631

-1776

3284

182

262

1247

1555

282

1455

121

1206

8462

266

-861

742

241

-491

12164

336

-10

-9

12898

476

-2723

7416

212

3176

-1782

3212

150

-530

281

467

-684

11473

-149

-219

12752

284

2364

5588

3150

1775

3294

186

-1350

1823

2175

-1475

6265

106

-1195

1428

3166

-1779

3244

-603

364

1764

-1328

7520

* Absolute contribution (acor) is 1360 for the class-98, followed by absolute contribution for: class-97 (1330.), class-96 (1126.), class-94 (529.), class-93 (430.), class-91 (91.), class-89 (83.), class-99 (61.), class-92 (4.), class-95 (2.), class-90 (1.).

Table 13 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 3

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

192

465

760

577

111

239

489

3522

182

262

784

615

112

576

759

9038

266

-1313

1725

560

-748

12724

336

-34

-29

12899

476

-345

119

-226

3263

150

-346

120

199

-446

11672

165

244

12811

284

1416

2005

1130

1063

4424

186

-75

-82

6272

106

-844

712

1578

-1256

4821

-230

257

-507

7776

* Absolute contribution (acor) 1360. class-98 followed by absolute contribution for: class-97 (1330.), class-96 (1126.), class-94 (529.), class-93 (430.), class-91 (91.), class-89 (83.), class-99 (61.), class-92 (4.), class-95 (2.), class-90 (1.).

Table 14 Relative mutual contributions of factors (from 1 to 3) per class

kls

knot1

knot2

Q(n)

inr

+inr

192

122

182

113

111

Significance of dipole association coefficient (class) Q (n) is the highest for the class-99 (192.) followed by: class-98 (182.), class-94 (80.), class-93 (74.), class-89 (70.), class-96 (65.), class-90 (38.), class-97 (36.), class-95 (29.), class-91 (27.), class-92 (16.).

* Inertia 39. class-99 this means that it stands out most prominently, it is followed by: class-98 (16.), class-97 (9.), class-96 (7.), class-95 (6.), class-94 (4.), class-93 (3.), class-92 (2.), class-91 (2.), class-90 (1.), class-89 (1.).

* The contribution of the 1st- isolated factor to the class-98 is 113, this means that examinees that belong to the class-98 have anthropometric and linear hepatic measurements characteristics of the 1st-factor structure, followed by: class-97 (111.), class-96 (94.), class-94 (44.), class-93 (36.), class-91 (8.), class-89 (7.), class-99 (5.), class-95 (0.), class-92 (0.), class-90 (0.). The contribution of the 2nd- isolated factor to the class-99 is 122. followed by: class-98 (24.), class-95 (18.), class-92 (7.), class-91 (4.), class-90 (4.), class-97 (2.), class-94 (2.), class-89 (2.), class-96 (0.), class-93 (0.). The contribution of the 3rd- isolated factor to the class-99 is 9., followed by: class-98 (9.), class-97 (5.), class-92 (3.), class-90 (2.), class-94 (1.), class-96 (0.), class-95 (0.), class-93 (0.), class-91 (0.), class-89 (0.).

*The highest contribution of the factor to the class-99 (122.) makes 1st- factor, this means that mentioned structure have examinees of the observed class. The same can be said, with less contribution, for characteristics: factor-2 (9.), factor-3 (5.). The contribution to the class-98 (113.) belongs to 1.- factor and factor-2 (24.), factor-3 (9.). The contribution to the class-97 (111.) belongs to 1.- factor and factor-2 (5.), factor-3 (2.). The contribution to the class-96 (94.) belongs to 1.- factor and factor-2 (0.), factor-3 (0.). The contribution to the class-95 (18.) belongs to 1.- factor and factor-2 (0.), factor-3 (0.). The contribution to the class-94 (44.) belongs to 1.- factor and factor-2 (2.), factor-3 (1.). The contribution to the class-93 (36.) belongs to 1.- factor and factor-2 (0.), factor-3 (0.). The contribution to the class-92 (7.) belongs to 1.- factor and factor-2 (3.), factor-3 (0.). The contribution to the class-91 (8.) belongs to 1.- factor and factor-2 (4.), factor-3 (0.). The contribution to the class-90 (4.) belongs to 1.- factor and factor-2 (2.), factor-3 (0.). The contribution to the class-89 (7.) belongs to 1.- factor and factor-2 (2.), factor-3 (0.).

Presentation of isolated classes

Significance of dipole association coefficient (class) Q(n) is the highest for the class-94 (80.) followed by: class-96 (65.), class-97 (36.).

* Inertia 9. class-97 it stands out most prominently, it is followed by: class-96 (7.), class-94 (4.).

* The contribution of the 1st- isolated factor to the class-97 is 111, followed by: class-96 (94.), class-94 (44.). The contribution of the 2nd- isolated factor to the class-97 is 2. followed by: class-94 (2.), class-96 (0.). The contribution of the 3rd- isolated factor to the class-97 is 5. followed by: class-94 (1.), class-96 (0.).

*, factor-2 (9.), factor-3 (9.), factor-2 (5.), factor-3 (0.), factor-3 (0.), factor-3 (1.), factor-3 (0.), factor-2 (3.), factor-3 (0.), factor-2 (2.), factor-3 (0.).

Structure of 3 isolated factors for the anthropometric and linear hepatic measurements

Table 15 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

515

1000

BMI

891

1000

D-il

378

503

386

1000

ApBo

271

695

662

386

1000

TvBo

303

818

791

445

816

1000

MxAp

225

636

620

457

659

623

1000

MxCo

135

-71

-34

-79

1000

MxCr

264

388

300

173

384

287

447

1000

MxCc

285

469

388

291

472

382

591

949

1000

Comx

195

-29

-10

-54

-133

916

1000

Vcal

303

523

443

240

469

482

616

614

709

751

541

1000

We found the strongest correlations (949) between Max CC (MxCc) and Maximal Crainocaudal (MxCr) and the strongest negative correlation is -133 between Cormax LL (Comx) and Maximal Ap (MxAp).

Table 16 The characteristic square of a factor and the percentage contribution

sqare

sum

5.530

46.083

2.326

19.380

65.463

1.455

12.129

77.592

1.046

8.714

86.306

.610

5.087

91.393

.427

3.561

94.954

.355

2.961

97.915

.129

1.076

98.991

.083

.688

99.679

.032

.263

99.942

.005

.042

99.984

.002

.016

100.000

Percentage representation of the characteristic squares falls in the range between .016% and 46.083%. The new structure is consisted of 3 isolated factors which contain 77.592 % information from the whole sample.

Table 17 Structure of 3 isolated factors for the anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

239

451

204

145

-121

wgt

884

880

775

140

-155

-291

BMI

760

783

613

111

-257

-285

D-il

393

545

297

-214

-225

ApBo

723

802

643

116

-245

-141

TvBo

849

829

687

124

-166

-367

134

MxAp

708

802

643

116

-235

102

MxCo

950

172

925

856

368

-255

MxCr

938

659

435

167

689

475

327

MxCc

966

751

565

102

106

625

390

268

Comx

949

149

915

837

360

-300

Vcal

952

786

618

112

542

294

126

198

12.0

1000

The factor structure for anthropometric and linear hepatic measurements

The entire sample that consisted of 12 anthropometric and linear hepatic measurements is reduced to 3 isolated factors. Contribution of isolated factor (qlt) is significant for 10 anthropometric and linear hepatic measurements.

* Structure of the 1st- isolated factor is formed of 8 anthropometric and linear hepatic measurements: weight (wgt) with factor contribution (cor) 776, Transverse body dimension (TvBo) 687, AP body dimension (ApBo) 643, Maximal Ap (MxAp) 643, liver volume (calculated by formula) (Vcal) 619, BMI (BMI) 613, Max CC (MxCc) 565, Maximal Crainocaudal (MxCr) 435. Latent variable is: Diaphragm to iliac (D-il) 297. Weighting is in concordance with: Transverse body dimension, AP body dimension, Maximal Ap, liver volume (calculated by formula), BMI, Max CC, Maximal Crainocaudal, Diaphragm to iliac.

* Structure of the 2nd- isolated factor is formed of 2 anthropometric and linear hepatic measurements: Maximal Coronal (MxCo) with factor contribution (cor) 856 and Cormax LL (Comx) 837. Latent variables are: liver volume (calculated by formula) (Vcal) 294. Association Maximal Coronal is in concordance with: Cormax LL, liver volume (calculated by formula).

* Structure of the 3rd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: Maximal Crainocaudal (MxCr) with factor contribution (cor) 476. Latent variables are: Max CC (MxCc) 391. Association of Maximal Crainocaudal is in concordance with: Max CC.

In forming the structure of two and more factors contribute, 3 anthropometric and linear hepatic measurements contribute most, in forming only one factor contribute 8 anthropometric and linear hepatic measurements, with low contribution without significance in forming the factor is 1 anthropometric and linear hepatic measurement. In forming the structure of isolated factors contribute 11 (91.67%) anthropometric and linear hepatic measurements.

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

Analizom from the sample consisting of 50 examinees revealed that in forming the structure of 3 isolated factors 33 (66.00%) have high contribution, 12 (24.00%) have intermediate contribution, 5 (10.00%) examinees are with low contribution, without significance.

1. – for 17 examinees (34.00%) anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 4 examinees (8.00%). For 8 we found direct proportionality, and 13 are inversely related.

2. – for 11 examinees (22.00%) anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure are 4 examinees (8.00%). For 7 we found direct proportionality, and 8 are inversely related.

3. – for 5 examinees (10.00%), anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure are 4 (8.00%). For 5 we found direct proportionality, and 4 are inversely related.

Concordance anthropometric and linear hepatic measurements with the structure: two and more factor have 1 examinee , one factor have 31 , latent agreement only have 7 examinees , with no agreement are 11 examinees.

It should be noted that 1 examinee stands out from the rest (inr)

Graph 5 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 6 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 7 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 8 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Table 18 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-0,::GrpD-0

.05

::GrpD-2,::GrpD-0

.09

::GrpD-0,::GrpD-0

.13

::GrpD-3,::GrpD-0

.15

::GrpD-2,::GrpD-3

.20

::GrpD-2,::GrpD-0

.38

::GrpD-2,::GrpD-0

.50

::GrpD-1,::GrpD-0

.61

::GrpD-1,::GrpD-0

1.00

::GrpD-1,::GrpD-0

1.80

::GrpD-1,::GrpD-2

2.50

From the dendrogram shown we found that the closest were groups ::GrpD-0 and:GrpD-0 with the distance.05. The biggest difference is between::GrpD-1 and:GrpD-2, distance 2.50.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3) ;;GrpD-0;; (4) ;;GrpD-0;; (5) ;;GrpD-0;; (6) ;;GrpD-0;; (7) ;;GrpD-0;; (8) ;;GrpD-0;; (9) ;;GrpD-0;; (10) ;;GrpD-0;; (11) ;;GrpD-0;; (12)

The mutual contribution of the division classes and factors structure for anthropometric and linear hepatic measurements

Table 19 Mutual contributions among division groups (3) and isolated factors structure

1-factor

2-factor

3-factor

mass

inr

kvl

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

::GrpD-1

320

1000

-1699

875

167

-10

643

125

::GrpD-2

260

101

1000

416

2043

895

467

-562

::GrpD-3

420

1000

1037

402

-1257

591

285

-142

As shown in Table 19 we found that the highest weight (mass) is 420. for class ;;GrpD-3;; this means that the biggest part of the sample belongs to one class, and it belongs to this class which corresponds to the specified weighting factor, and the next is for the class: ;;GrpD-1;; (320.), ;;GrpD-2;; (260.).

* Inertia (inr) of the class ;;GrpD-2;; is 101. It means that this class stands out from the rest, and the next is for the class: ;;GrpD-3;; (94.), ;;GrpD-1;; (88.).

* Relative contribution (cor) 1. – of the axis to the class ;;GrpD-1;; is 875- high, which means that the axis has the most information about that class, then for: ;;GrpD-3;; (402.-intermediate), ;;GrpD-2;; (37.-without significance). Relative contribution 2. – of the axis to the class ;;GrpD-2;; is 895. high, then for: ;;GrpD-3;; (591.-intermediate), ;;GrpD-1;; (0.-without significance). Relative contribution 3. – of the axis to the class ;;GrpD-1;; is 125. without significance, then for: ;;GrpD-2;; (68.-without significance), ;;GrpD-3;; (8.-without significance).

* Relative contribution of the class ;;GrpD-1;; to inertia of the 1. – axis is 167, then for: ;;GrpD-3;; (82.), ;;GrpD-2;; (8.). Relative contribution of the class ;;GrpD-2;; to inertia of the 2. – axis is 467, then for: ;;GrpD-3;; (285.), ;;GrpD-1;; (0.). Relative contribution of the class ;;GrpD-1;; to inertia of the 3rd – axis is 91, then for: ;;GrpD-2;; (56.), ;;GrpD-3;; (6.).

* The association of classes on the 2nd axis is proportional to the classes ;;GrpD-1;;, ;;GrpD-3;;, and inversely proportional for the class ;;GrpD-2;;.

Table 20 Contribution of each factor to a class in :‰:

::GrpD-1

875

125

::GrpD-2

895

::GrpD-3

402

591

* The factor F1 gives the highest contribution to the class ::GrpD-1 (875‰) then F3 (125‰) which contributes 7.0 times less.

Table 21 Mahalanobis distance between ;;GrpD;; in relation to anthropometric and linear hepatic measurements

::GrpD-1

::GrpD-2

::GrpD-3

::GrpD-1

.00

3.29

2.38

::GrpD-2

3.29

.00

4.59

::GrpD-3

2.38

4.59

.00

By calculating the Mahalanobis distance between ;; GrpD ;; we obtained another indicator of similarities or differences. Distances of different spaces can be compared. According to the results in the table we can say that the distance is minimal between ;;GrpD;;: ;;GrpD-3;; and ;;GrpD-1;; (::GrpD-3 and:GrpD-1 (2.38) (bigger) and the farthest are;;GrpD;; : ;;GrpD-3;; and ;;GrpD-2;; (::GrpD-3 and:GrpD-2 (4.59) (bigger).

Table 22 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-1,::GrpD-3

2.38

::GrpD-1,::GrpD-2

4.17

From the dendrogram shown we found that the closest were groups ::GrpD-1 and:GrpD-3 with the distance 2.38, and the biggest difference is between::GrpD-1 and:GrpD-2, distance 4.17.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3)

Analysis of the structure anthropometric and linear hepatic measurements

In accordance to the previously established design of the study, it was planned to extract optimal number of factors, using factor analysis of principal components , from 12 anthropometric and linear hepatic measurements: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal). The aim is to find the associations between individual variables, to determine the contribution of each factor to a variable, contribution of each variable to a factor, to apply complementary analyses and to present the results Graphically. The coordinates of the variables for anthropometric and linear hepatic measurements will be presented to determine their position in an isolated structure.

Structure of 3 isolated factors for anthropometric and linear hepatic measurements

Table 23 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

373

1000

BMI

-466

621

1000

D-il

-46

455

459

1000

ApBo

-54

599

597

469

1000

TvBo

677

564

524

851

1000

MxAp

385

363

320

491

473

1000

MxCo

136

-76

-37

-75

1000

MxCr

238

-74

113

146

113

1000

MxCc

225

190

256

176

214

283

926

1000

Comx

149

160

233

193

735

105

150

1000

Vcal

204

251

100

284

235

292

557

609

658

676

514

1000

We found the strongest correlations (926) between Max CC (MxCc) and Maximal Crainocaudal (MxCr), the strongest negative correlation is -466 between BMI (BMI) and height (hgt).

Table 24 The characteristic square of a factor and the percentage contribution

sqare

sum

4.191

34.925

2.638

21.985

56.910

1.623

13.523

70.433

1.225

10.205

80.638

.772

6.430

87.068

.567

4.729

91.796

.495

4.123

95.920

.277

2.311

98.230

.133

1.110

99.340

.058

.484

99.824

.017

.145

99.969

.004

.031

100.000

Percentage representation of the characteristic squares fall in the range between .031% to 34.925%. The new structure is consisted of 3 isolated factors which contain 70.433 % information from the whole sample.

Table 25 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

228

-142

445

198

-96

wgt

623

-738

544

130

-280

BMI

716

-591

349

-600

360

136

D-il

475

-654

427

102

-200

ApBo

766

-752

566

135

-447

199

-15

TvBo

784

-805

649

155

-363

131

MxAp

477

-650

422

101

-125

-199

MxCo

894

-256

556

309

117

721

520

320

MxCr

887

-426

181

656

430

163

-525

276

170

MxCc

895

-564

318

562

316

120

-511

261

161

Comx

837

-389

151

436

190

704

495

305

Vcal

871

-705

497

119

609

371

140

12.0

1000

The factor structure for anthropometric and linear hepatic measurements

Whole sample that consisted of 12 anthropometric and linear hepatic measurements is reduced to 3 isolated factors. Contribution of isolated factor (qlt) is significant for 11 anthropometric and linear hepatic measurement.

* The communality is higher for: Max CC (MxCc) 895, Maximal Coronal (MxCo) 894, Maximal Crainocaudal (MxCr) 887, liver volume (calculated by formula) (Vcal) 871, Cormax LL (Comx) 837, Transverse body dimension (TvBo) 784, AP body dimension (ApBo) 766, BMI (BMI) 716, weight (wgt) 623.

* Intermediate communality shows that the structure of 3 isolated factors contain intermediate information about 2 anthropometric and linear hepatic measurements: Maximal Ap (MxAp) 477, Diaphragm to iliac (D-il) 475.

* Decreased communality shows that the structure of 3 isolated factors does not contain enough information about 1 anthropometric and linear hepatic measurement: height (hgt) 228

The variables that contribute in forming the structure of each isolated factor are: Max CC, Maximal Coronal, Maximal Crainocaudal, liver volume (calculated by formula), Cormax LL, Transverse body dimension, AP body dimension, BMI, weight, Maximal Ap, Diaphragm to iliac, the variables that do not contribute to factor structure are: height.

* Structure of the 1st- isolated factor is formed of 6 anthropometric and linear hepatic measurements: Transverse body dimension (TvBo) with factor contribution (cor) 649, AP body dimension (ApBo) 567, weight (wgt) 544, liver volume (calculated by formula) (Vcal) 498, Diaphragm to iliac (D-il) 428, Maximal Ap (MxAp) 423. Latent variables are: BMI (BMI) 349, Max CC (MxCc) 319. Association of the Transverse body dimension is in concordance with: AP body dimension, weight, liver volume (calculated by formula), Diaphragm to iliac, Maximal Ap, BMI, Max CC.

* Structure of the 2nd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: Maximal Crainocaudal (MxCr) with factor contribution (cor) 431. Latent variables are: liver volume (calculated by formula) (Vcal) 371, BMI (BMI) 360, Max CC (MxCc) 316, Maximal Coronal (MxCo) 309. Association of the Maximal Crainocaudal is in concordance with: liver volume (calculated by formula), Max CC, Maximal Coronal. Association Maximal Crainocaudal is inversely proportional with: BMI.

* Structure of the 3rd- isolated factor is formed of 2 anthropometric and linear hepatic measurements: Maximal Coronal (MxCo) with factor contribution (cor) 520, Cormax LL (Comx) 496. Latent variables are: Maximal Crainocaudal (MxCr) 276. Association Maximal Coronal is in concordance with: Cormax LL. Association Maximal Coronal is inversely proportional with: Maximal Crainocaudal.

* Several factors contribute to variable for: BMI, factor-1 (349), factor-2 (360), Maximal Coronal, factor-2 (309), factor-3 (520), Maximal Crainocaudal, factor-2 (431), factor-3 (276), Max CC, factor-1 (319), factor-2 (316), liver volume (calculated by formula), factor-1 (498), factor-2 (371).

In forming the structure of two and more factors contribute contribute 5 anthropometric and linear hepatic measurements, in forming only one factor contribute 6 anthropometric and linear hepatic measurements, with low contribution without significance in forming the factor is 1 anthropometric and linear hepatic measurement. In forming the structure of isolated factors contribute 11 (91.67%) anthropometric and linear hepatic measurements.

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

The analysis of the sample consisting of 106 revealed that in forming the structure of 3 isolated factors 70 (66.04%) examinees have high contribution, intermediate contribution have 23 (21.70%), with low contribution without significance are 13 (12.26%).

1. – for 43 (40.57%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 16 (15.09%) examinees. For 24 we found direct proportionality, and for 35 are inversely related.

2. – for 17 (16.04%) anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure are 10 (9.43%) examinees. For 13 examinees we found direct proportionality, and 14 are inversely related.

3. – for 10 (9.43%) anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure are 10 (9.43%) examinees. For 11 we found direct proportionality, and 9 are inversely related.

Concordance anthropometric and linear hepatic measurements with the structure: two and more factor have 1 examinee, one factor have 68 examinees , latent agreement only have 24, and with no agreement are 13 examinees .

It should be noted that 1 examinee stands out from the rest (inr)

Graph 9 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 10 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 11 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 12 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Clustering on factors for anthropometric and linear hepatic measurements

In this part of the study we clusterised 106 based on 3 isolated factors from 12 anthropometric and linear hepatic measurements.

Sum of the levels of measures1.152

Table 27 Levels of grouping on the isolated factors

class

distance

class1

class2

nbr.elemn.

211

449

210

208

106

210

239

209

207

209

203

206

208

205

204

207

202

198

206

197

196

205

201

194

204

199

193

203

184

200

202

190

195

201

174

189

200

179

192

Group-1 (knot 207) that contains 22 examinees, is consisted of sublevels, knots 202 and 198, the distance between them is 54. Group-2 (knot 208) contains 45 examinees, is consisted of sublevels, knots 205 and 204, the distance between them is 71. Group-3 (knot 209) that contains 39 examinees, is consisted of sublevels, knots 203 and 206, the distance between them is 85.

Mutual contributions of hierarchical classification classes and isolated factor structures for anthropometric and linear hepatic measurements

In this part of the study we analysed 11 higher classes of hierarchical classification and 3 isolated classes from the sample consisting of 106 in relation to 3 isolated factors structure for the anthropometric and linear hepatic measurements. Isolated classes are: 207, 208, 209.

Centers of hierarchical classification classes and isolated factors

Table 28 Centers of 3 hierarchical classification classes in relation to 3 isolated factors structures

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qlt

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

211

210

208

1000

904

210

209

207

575

592

171

-1446

170

287

-104

-45

209

203

206

368

369

301

-1457

176

186

-1225

125

209

-55

208

205

204

425

350

391

1960

389

141

207

202

198

208

242

398

-1427

145

101

1883

253

279

-27

206

197

196

132

211

568

-3079

494

299

-1191

205

201

194

104

137

600

2526

402

158

1718

186

116

-437

204

199

193

321

218

409

1778

387

242

-369

222

203

184

200

236

165

221

-549

-1244

184

138

-88

202

190

195

183

603

-2311

229

120

2887

358

298

608

201

174

189

725

3308

645

172

1039

-520

As shown in Table 28 we found that the highest weight coefficient is 425. for isolated class-208, This means that the biggest part of the sample which belongs to one class, belongs to this class which corresponds to the specified weighting factor, it is followed by: class-209 (368.), class-207 (208.).

* Inertia 904. class-211 this means that it stands out most prominently, it is followed by: class-210 (592.), class-209 (369.), class-208 (350.), class-207 (242.), class-204 (218.), class-206 (211.), class-202 (183.), class-203 (165.), class-205 (137.), class-201 (93.).

* Contribution of isolated factors 725. is high, for class-201 this means that isolated factors gives the most information to this class, then for: class-202 (603.-high), class-205 (600.-high), class-206 (568.-intermediate), class-204 (409.-intermediate), class-207 (398.-low), class-208 (391.-low), class-209 (301.-low), class-203 (221.-without significance), class-210 (171.-without significance), class-211 (0.-without significance).

* Relative contribution of the 1st-isolated factor to the center of the class-201 is 645- high, this means that factor gives the most information to this class, then for: center of the class-206 (494.-intermediate), center of the class-205 (402.-intermediate), center of the class-208 (389.-low), center of the class-204 (387.-low), center of the class-202 (229.-without significance), center of the class-209 (176.-without significance), center of the class-210 (170.-without significance), center of the class-207 (145.-without significance), center of the class-203 (36.-without significance), center of the class-211 (0.-without significance). Relative contribution of the 2nd-isolated factor to the center of the class-202 is 358- low, then for: center of the class-207 (253.-without significance), center of the class-205 (186.-without significance), center of the class-203 (184.-without significance), center of the class-209 (125.-without significance), center of the class-206 (74.-without significance), center of the class-201 (64.-without significance), center of the class-204 (17.-without significance), center of the class-208 (2.-without significance), center of the class-210 (1.-without significance), center of the class-211 (0.-without significance). Relative contribution of the 3rd-isolated factor to the center of the class-202 is 16. without significance, then for: center of the class-201 (16.-without significance), center of the class-205 (12.-without significance), center of the class-204 (6.-without significance), center of the class-203 (1.-without significance), center of the class-211 (0.-without significance), center of the class-210 (0.-without significance), center of the class-209 (0.-without significance), center of the class-208 (0.-without significance), center of the class-207 (0.-without significance), center of the class-206 (0.-without significance).

* Association of the cluster for the 1st- factors structure is proportional between classes-211, class-209, class-203, class-211, class-208, class-207, inversely proportional with, class-208, class-205, class-204, class-201.

* Association of the cluster for the 2nd- factors structure is proportional between classes-211, class-209, class-211, class-209, class-208, inversely proportional with, class-208, class-207, class-205, class-202, class-201.

* Association of the cluster for the 3rd- factors structure is proportional between classes-211, class-209, class-203, class-210, class-208, class-206, inversely proportional with, class-208, class-206, class-204, class-202.

Table 29 Center of hierarchical classification classes in relation to the factors axis 1 (factor variance: 4.1910)

knot

knot1

knot2

weight

inr

dst

(F1)2

acor

cor

ctr

cos

+cos2

211

210

208

1000

904

10848

210

209

207

575

592

12336

-1446

2092

1204

170

287

-412

170

209

203

206

368

369

12042

-1457

2123

781

176

186

-420

176

208

205

204

425

350

9889

1960

3844

1632

389

624

389

207

202

198

208

242

14008

-1427

2036

423

145

101

-381

145

206

197

196

132

211

19194

-3079

9479

1252

494

299

-703

494

205

201

194

104

137

15881

2526

6381

662

402

158

634

402

204

199

193

321

218

8170

1778

3160

1013

387

242

622

387

203

184

200

236

165

8399

-549

301

-190

202

190

195

183

23289

-2311

5341

504

229

120

-479

229

201

174

189

16963

3308

10942

723

645

172

803

645

As shown in Table 29 the greatest distance (dst) 23289. between the center of the cloud and the center of the class is 202, it is followed by: class-206 (19194.), class-201 (16963.), class-205 (15881.), class-207 (14008.), class-210 (12336.), class-209 (12042.), class-211 (10848.), class-208 (9889.), class-203 (8399.), class-204 (8170.).

* Absolute contribution (acor) 1632. Class is

208 followed by absolute contribution for: class-206 (1252.), class-210 (1204.), class-204 (1013.), class-209 (781.), class-201 (723.), class-205 (662.), class-202 (504.), class-207 (423.), class-203 (71.), class-211 (0.).

* The cosine of an angle (cos) 803. between the radius of the center of the class -201 and axis, class-206 (-703.), class-205 (634.), class-208 (624.), class-204 (622.), class-202 (-479.), class-209 (-420.), class-210 (-412.), class-207 (-381.), class-203 (-190.), class-211 (0.).

Table 30 Center of hierarchical classification classes in relation to the factors axis 2 (factor variance: 2.6383)

knot

knot1

knot2

weight

inr

dst

(F2)2

acor

cor

ctr

cos

+cos2

211

210

208

1000

904

10848

210

209

207

575

592

12336

-104

-30

170

209

203

206

368

369

12042

-1225

1500

552

125

209

-353

301

208

205

204

425

350

9889

141

391

207

202

198

208

242

14008

1883

3544

736

253

279

503

398

206

197

196

132

211

19194

-1191

1419

187

-272

568

205

201

194

104

137

15881

1718

2951

306

186

116

431

588

204

199

193

321

218

8170

-369

136

-129

403

203

184

200

236

165

8399

-1244

1547

365

184

138

-429

220

202

190

195

183

23289

2887

8336

786

358

298

598

587

201

174

189

16963

1039

1079

252

709

* Absolute contribution (acor) 786. class-202 followed by absolute contribution for: class-207 (736.), class-209 (552.), class-203 (365.), class-205 (306.), class-206 (187.), class-201 (71.), class-204 (44.), class-208 (8.), class-210 (6.), class-211 (0.).

* The cosine of an angle (cos) 598. between the radius of the center of the class -202 and axis, class-207 (503.), class-205 (431.), class-203 (-429.), class-209 (-353.), class-206 (-272.), class-201 (252.), class-204 (-129.), class-208 (45.), class-210 (-30.), class-211 (0.).

Table 31 Center of hierarchical classification classes in relation to the factors axis 3 (factor variance: 1.6228)

knot

knot1

knot2

weight

inr

dst

(F3)2

acor

cor

ctr

cos

+cos2

211

210

208

1000

904

10848

210

209

207

575

592

12336

-45

-13

171

209

203

206

368

369

12042

-55

-16

301

208

205

204

425

350

9889

391

207

202

198

208

242

14008

-27

-7

398

206

197

196

132

211

19194

568

205

201

194

104

137

15881

-437

191

-110

600

204

199

193

321

218

8170

222

409

203

184

200

236

165

8399

-88

-31

221

202

190

195

183

23289

608

369

126

603

201

174

189

16963

-520

271

-126

725

* Absolute contribution (acor) 35. class-202 followed by absolute contribution for: class-205 (20.), class-201 (18.), class-204 (16.), class-208 (2.), class-203 (2.), class-210 (1.), class-209 (1.), class-211 (0.), class-207 (0.), class-206 (0.).

* The cosine of an angle (cos) 126. between the radius of the center of the class -202 and axis, class-201 (-126.), class-205 (-110.), class-204 (78.), class-203 (-31.), class-208 (19.), class-209 (-16.), class-210 (-13.), class-207 (-7.), class-206 (1.), class-211 (0.).

Analysis of differences between two nodes (dipoles) of hierarchical classification classes

Table 32 Dipoles of the 11 highest nodes in relation to the factors axes from 1 to 3

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qld

cod

ctd

cod

ctd

cod

ctd

211

210

208

1000

6352

-3407

6313

677

-245

-105

210

209

207

575

5358

-30

-3108

5357

486

-27

209

203

206

368

6360

2530

6349

129

-53

-94

208

205

204

425

5937

749

622

2087

4833

129

-659

482

207

202

198

208

7045

-1621

2510

1842

3240

1164

1294

206

197

196

132

5438

676

290

2841

5113

-237

205

201

194

104

5920

2150

3352

-1868

2530

-229

204

199

193

321

7220

-795

1823

1151

3820

-739

1577

203

184

200

236

7093

-887

2145

1140

3548

716

1400

202

190

195

9619

-1818

4165

-1210

1845

-1692

3610

201

174

189

6399

1290

2343

-1550

3382

693

675

As shown in Table() we found that Inertia of the dipole (ind) a(n) b(n) is 37, that is, the inertia of the whole system , class-211 , followed by dipoles: class-210 (20.), class-209 (7.), class-208 (6.), class-207 (4.), class-206 (3.), class-205 (3.), class-204 (2.), class-203 (2.), class-202 (2.), class-201 (1.).

* The quality of the observed factors (qld) 9619. is high, for class-202 (dipole) which represents the quality of the vector ab representation in the factors space of this research, the other qualities are for: class-204 (7220.-high), class-203 (7093.-high), class-207 (7045.-high), class-201 (6399.-high), class-209 (6360.-high), class-211 (6352.-high), class-208 (5937.-high), class-205 (5920.-high), class-206 (5438.-high), class-210 (5358.-high).

* Projection ab on the axis 1st-isolated factor, that is, the projection of the dipole class-211 is -3407, other dipole projections on the axis are: class-209 (2530.), class-205 (2150.), class-202 (-1818.), class-207 (-1621.), class-201 (1290.), class-203 (-887.), class-204 (-795.), class-208 (749.), class-206 (676.), class-210 (-30.). Projection ab on the axis 2nd-isolated factor, that is, the projection of the dipole class-210 is -3108, other dipole projections on the axis are: class-206 (2841.), class-208 (2087.), class-205 (-1868.), class-207 (1842.), class-201 (-1550.), class-202 (-1210.), class-204 (1151.), class-203 (1140.), class-211 (-245.), class-209 (-53.). Projection ab on the axis 3rd-isolated factor, that is, the projection of the dipole class-202 is -1692, other dipole projections on the axis are: class-207 (1164.), class-204 (-739.), class-203 (716.), class-201 (693.), class-208 (-659.), class-206 (-237.), class-205 (-229.), class-211 (-105.), class-209 (-94.), class-210 (-27.).

* Relative contribution of the 1st-factor axis (D1), dipole a(n) b(n) is class-209 is 6349. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-211 (6313.-high), class-202 (4165.-high), class-205 (3352.-high), class-207 (2510.-high), class-201 (2343.-high), class-203 (2145.-high), class-204 (1823.-high), class-208 (622.-high), class-206 (290.-low), class-210 (1.-without significance). Relative contribution of the 2nd-factor axis (D2), dipole a(n) b(n) is class-210 is 5357. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-206 (5113.-high), class-208 (4833.-high), class-204 (3820.-high), class-203 (3548.-high), class-201 (3382.-high), class-207 (3240.-high), class-205 (2530.-high), class-202 (1845.-high), class-211 (33.-without significance), class-209 (3.-without significance). Relative contribution of the 3rd-factor axis (D3), dipole a(n) b(n) is class-202 is 3610. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-204 (1577.-high), class-203 (1400.-high), class-207 (1294.-high), class-201 (675.-high), class-208 (482.-intermediate), class-205 (38.-without significance), class-206 (36.-without significance), class-209 (9.-without significance), class-211 (6.-without significance), class-210 (0.-without significance).

* Relative contribution of dipoles (ctd) class-211 to axis of the 1st-factor is 6313, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-209 (6349.), class-207 (2510.), class-205 (3352.), class-202 (4165.), class-204 (1823.), class-203 (2145.), class-208 (622.), class-201 (2343.), class-206 (290.), class-210 (1.). Relative contribution of dipoles (ctd) class-210 to axis of the 2nd-factor is 5357, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-208 (4833.), class-206 (5113.), class-207 (3240.), class-204 (3820.), class-205 (2530.), class-203 (3548.), class-201 (3382.), class-202 (1845.), class-211 (33.), class-209 (3.). Relative contribution of dipoles (ctd) class-207 to axis of the 3rd-factor is 1294, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-202 (3610.), class-204 (1577.), class-208 (482.), class-203 (1400.), class-201 (675.), class-211 (6.), class-206 (36.), class-205 (38.), class-210 (0.), class-209 (9.).

Table 33 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 1

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

211

210

208

244

449

-3407

11606

2835

6313

677

-2513

6313

210

209

207

133

416

-30

-23

209

203

206

232

2530

6400

542

6349

129

2520

6349

208

205

204

166

749

560

622

789

622

207

202

198

260

-1621

2628

135

2510

-1584

2510

206

197

196

266

676

457

290

538

290

205

201

194

319

2150

4623

111

3352

1831

3352

204

199

193

-795

632

1823

-1350

1823

203

184

200

-887

786

2145

-1465

2145

202

190

195

198

-1818

3305

4165

-2041

4165

201

174

189

174

1290

1664

2343

1531

2343

As shown in Table() the greatest distance (dst) 449. between the center of the cloud and the center of the class-211 , it is followed by: class-210 (416.), class-205 (319.), class-206 (266.), class-207 (260.), class-209 (232.), class-202 (198.), class-201 (174.), class-208 (166.), class-203 (90.), class-204 (76.).

* Absolute contribution (acor) 2835. class-211 followed by absolute contribution for: class-209 (542.), class-207 (135.), class-205 (111.), class-202 (78.), class-203 (46.), class-208 (44.), class-204 (44.), class-201 (27.), class-206 (10.), class-210 (0.).

* The cosine of an angle (cos) 2520. between the radius of the center of the class -209 and axis, class-211 (-2513.), class-202 (-2041.), class-205 (1831.), class-207 (-1584.), class-201 (1531.), class-203 (-1465.), class-204 (-1350.), class-208 (789.), class-206 (538.), class-210 (-23.).

Table 34 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 2

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

211

210

208

244

449

-245

-181

6346

210

209

207

133

416

-3108

9657

1281

5357

486

-2315

5358

209

203

206

232

-53

-52

6352

208

205

204

166

2087

4355

341

4833

129

2198

5455

207

202

198

260

1842

3392

175

3240

1800

5751

206

197

196

266

2841

8069

179

5113

2261

5403

205

201

194

319

-1868

3489

2530

-1591

5882

204

199

193

1151

1324

3820

1955

5643

203

184

200

1140

1300

3548

1884

5693

202

190

195

198

-1210

1464

1845

-1358

6010

201

174

189

174

-1550

2403

3382

-1839

5724

Table 35 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 3

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

211

210

208

244

449

-105

-78

6352

210

209

207

133

416

-27

-20

5358

209

203

206

232

-94

-93

6360

208

205

204

166

-659

434

482

-694

5937

207

202

198

260

1164

1355

1294

1138

7045

206

197

196

266

-237

-188

5438

205

201

194

319

-229

-195

5920

204

199

193

-739

547

1577

-1256

7220

203

184

200

716

513

1400

1183

7093

202

190

195

198

-1692

2864

3610

-1900

9619

201

174

189

174

693

480

675

822

6399

Table 36 Relative mutual contributions of factors (from 1 to 3) per classes

kls

knot1

knot2

Q(n)

inr

+inr

211

210

208

244

236

210

209

207

133

107

209

203

206

208

205

204

207

202

198

206

197

196

205

201

194

204

199

193

203

184

200

202

190

195

201

174

189

Significance of dipole association coefficient (class) Q(n) is the highest for the class-211 (244.) followed by: class-210 (133.), class-209 (85.), class-208 (78.), class-204 (70.), class-203 (58.), class-207 (51.), class-205 (24.), class-202 (24.), class-206 (22.), class-201 (16.).

* Inertia 37. class-211 this means that it stands out most prominently, it is followed by: class-210 (20.), class-209 (7.), class-208 (6.), class-207 (4.), class-206 (3.), class-205 (3.), class-204 (2.), class-203 (2.), class-202 (2.), class-201 (1.).

* The contribution of the 1st- isolated factor to the class-211 is 236, this means that examinees who belong to the class-211 have anthropometric and linear hepatic characteristics of the 1st-factors structure, followed by: class-209 (45.), class-207 (11.), class-205 (9.), class-202 (6.), class-208 (4.), class-204 (4.), class-203 (4.), class-201 (2.), class-206 (1.), class-210 (0.). The contribution of the 2nd- isolated factor to the class-210 is 107. followed by: class-208 (28.), class-207 (15.), class-206 (15.), class-204 (8.), class-205 (7.), class-203 (6.), class-202 (3.), class-201 (3.), class-211 (1.), class-209 (0.). The contribution of the 3rd- isolated factor to the class-207 is 6. followed by: class-202 (6.), class-208 (3.), class-204 (3.), class-203 (2.), class-201 (1.), class-211 (0.), class-210 (0.), class-209 (0.), class-206 (0.), class-205 (0.).

*The highest contribution of the factor to the class-211 (236.) has the 1st- factor, this means that mentioned structure have examinees of the observed class. The same can be said, with less contribution, for characteristics: factor-2 (1.), factor-3 (0.). The contribution to the class-210 (107.) belongs to 1.- factor and factor-2 (0.), factor-3 (0.). The contribution to the class-209 (45.) belongs to 1.- factor and factor-2 (0.), factor-3 (0.). The contribution to the class-208 (28.) belongs to 1.- factor and factor-2 (4.), factor-3 (3.). The contribution to the class-207 (15.) belongs to 1.- factor and factor-2 (11.), factor-3 (6.). The contribution to the class-206 (15.) belongs to 1.- factor and factor-2 (1.), factor-3 (0.). The contribution to the class-205 (9.) belongs to 1.- factor and factor-2 (7.), factor-3 (0.). The contribution to the class-204 (8.) belongs to 1.- factor and factor-2 (4.), factor-3 (3.). The contribution to the class-203 (6.) belongs to 1.- factor and factor-2 (4.), factor-3 (2.). The contribution to the class-202 (6.) belongs to 1.- factor and factor-2 (6.), factor-3 (3.). The contribution to the class-201 (3.) belongs to 1.- factor and factor-2 (2.), factor-3 (1.).

Presentation of isolated classes

Significance of dipole association coefficient (class) Q(n) is the highest for the class-209 (85.) followed by: class-208 (78.), class-207 (51.).

* Inertia 7. class-209 this means that it stands out most prominently, it is followed by: class-208 (6.), class-207 (4.).

* The contribution of the 1st- isolated factor to the class-209 is 45. followed by: class-207 (11.), class-208 (4.). The contribution of the 2nd- isolated factor to the class-208 is 28. followed by: class-207 (15.), class-209 (0.). The contribution of the 3rd- isolated factor to the class-207 is 6. followed by: class-208 (3.), class-209 (0.).

*, factor-3 (0.), factor-3 (0.), factor-3 (0.), factor-3 (3.), factor-3 (6.), factor-3 (0.), factor-3 (0.), factor-3 (3.), factor-3 (2.), factor-2 (6.), factor-3 (1.).

Structure 3 isolated factor anthropometric and linear hepatic measurements

Table 37 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

373

1000

BMI

-466

621

1000

D-il

-46

455

459

1000

ApBo

-54

599

597

469

1000

TvBo

677

564

524

851

1000

MxAp

385

363

320

491

473

1000

MxCo

136

-76

-37

-75

1000

MxCr

238

-74

113

146

113

1000

MxCc

225

190

256

176

214

283

926

1000

Comx

149

160

233

193

735

105

150

1000

Vcal

204

251

100

284

235

292

557

609

658

676

514

1000

We found the strongest correlations (926) between Max CC (MxCc) and Maximal Crainocaudal (MxCr) . The strongest negative correlation is -466 between BMI (BMI) and height (hgt).

Table 38 The characteristic square of a factor and the percentage contribution

sqare

sum

4.191

34.925

2.638

21.985

56.910

1.623

13.523

70.433

1.225

10.205

80.638

.772

6.430

87.068

.567

4.729

91.796

.495

4.123

95.920

.277

2.311

98.230

.133

1.110

99.340

.058

.484

99.824

.017

.145

99.969

.004

.031

100.000

Percentage representation of the characteristic squares fall in the range between .031% do 34.925%. The new structure is consisted of 3 isolated factors which contain 70.433 % information from the whole.

Table 39 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

228

-142

445

198

-96

wgt

623

-738

544

130

-280

BMI

716

-591

349

-600

360

136

D-il

475

-654

427

102

-200

ApBo

766

-752

566

135

-447

199

-15

TvBo

784

-805

649

155

-363

131

MxAp

477

-650

422

101

-125

-199

MxCo

894

-256

556

309

117

721

520

320

MxCr

887

-426

181

656

430

163

-525

276

170

MxCc

895

-564

318

562

316

120

-511

261

161

Comx

837

-389

151

436

190

704

495

305

Vcal

871

-705

497

119

609

371

140

12.0

1000

The factor structure anthropometric and linear hepatic measurements

Whole sample that consisted of 12 anthropometric and linear hepatic measurements was reduced to 3 isolated factorss. Contribution of isolated factor (qlt) is significant for 11 anthropometric and linear hepatic measurement.

* Decreased communality shows that the structure of 3 isolated factors does not contain enough information about 1 anthropometric and linear hepatic measurement: height (hgt) 228

* Structure of the 1st- isolated factor is formed of 6 anthropometric and linear hepatic measurements: Transverse body dimension (TvBo) with factor contribution (cor) 649, AP body dimension (ApBo) 567, weight (wgt) 544, liver volume (calculated by formula) (Vcal) 498, Diaphragm to iliac (D-il) 428, Maximal Ap (MxAp) 423. Latent variables are: BMI (BMI) 349, Max CC (MxCc) 319. Association Transverse body dimension is in concordance with: AP body dimension, weight, liver volume (calculated by formula), Diaphragm to iliac, Maximal Ap, BMI, Max CC.

* Structure of the 2nd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: Maximal Crainocaudal (MxCr) with factor contribution (cor) 431. Latent variables are: liver volume (calculated by formula) (Vcal) 371, BMI (BMI) 360, Max CC (MxCc) 316, Maximal Coronal (MxCo) 309. Association Maximal Crainocaudal is in concordance with: liver volume (calculated by formula), Max CC, Maximal Coronal. Association Maximal Crainocaudal is inversely proportional with: BMI.

In forming the structure of two and more factors contribute 5 anthropometric and linear hepatic measurements, in forming only one factor contribute 6 anthropometric and linear hepatic measurements, with low contribution without significance in forming the factor is 1 anthropometric and linear hepatic measurement. In forming the structure of isolated factors contribute 11 (91.67%) anthropometric and linear hepatic measurements.

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

The analysis of the sample consisting of 106 revealed that in forming the structure of 3 isolated factors 70 (66.04%) have high contribution, 23 (21.70%) have intermediate contribution, with low contribution without significance were 13 (12.26%) examinees.

1. – for 43 (40.57%) anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure16 (15.09%). For 24 we found direct proportionality, and for 35 are inversely related.

2. – for 17 (16.04%) anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure10 (9.43%). For 13 we found direct proportionality, and for 14 are inversely related.

3. – for 10 (9.43%) anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure10 (9.43%). For 11 we found direct proportionality, and for 9 are inversely related.

Concordance of the anthropometric and linear hepatic measurements with the structure: two and more factor have 1 examinee , one factor have 68 examinees , latent agreement only have 24 examinees , with no agreement are 13 examinees.

It should be noted that 1 examinee stands out from the rest (inr)

Graph 13 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 14 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 15 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 16 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Table 40 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-2,::GrpD-0

.12

::GrpD-2,::GrpD-0

.16

::GrpD-0,::GrpD-0

.17

::GrpD-0,::GrpD-0

.18

::GrpD-2,::GrpD-0

.23

::GrpD-2,::GrpD-0

.41

::GrpD-2,::GrpD-3

.46

::GrpD-1,::GrpD-0

.60

::GrpD-1,::GrpD-0

.74

::GrpD-1,::GrpD-0

1.69

::GrpD-1,::GrpD-2

3.34

From the dendrogram shown we found that the closest were groups ::GrpD-2 and:GrpD-0 with the distance 12. The biggest difference is between::GrpD-1 and:GrpD-2 with the distance 3.34.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3) ;;GrpD-0;; (4) ;;GrpD-0;; (5) ;;GrpD-0;; (6) ;;GrpD-0;; (7) ;;GrpD-0;; (8) ;;GrpD-0;; (9) ;;GrpD-0;; (10) ;;GrpD-0;; (11) ;;GrpD-0;; (12)

The mutual contribution of the division classes and factors structure for anthropometric and linear hepatic measurements

Table 41 Mutual contributions among division groups (3) and isolated factors structure

1-factor

2-factor

3-factor

mass

inr

kvl

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

::GrpD-1

208

1000

-1427

365

101

1883

635

279

-27

::GrpD-2

425

137

1000

1960

994

389

141

::GrpD-3

368

111

1000

-1457

585

186

-1225

414

209

-55

As shown in Table 41 we found that the highest weight was 425. for the class ;;GrpD-2;; This means that the biggest part of the sample which belongs to one class, belongs to this class which corresponds to the specified weighting factor, and the next is for the class: ;;GrpD-3;; (368.) and ;;GrpD-1;; (208.).

* Inertia (inr) of the class ;;GrpD-2;; is 137. It means that this class stands out from the rest, and the next is for class: ;;GrpD-3;; (111.), ;;GrpD-1;; (97.).

* Relative contribution (cor) 1. – of the axis to the class ;;GrpD-2;; is 994. high, which means that the axis has the most information about that class, then for: ;;GrpD-3;; (585.-intermediate), ;;GrpD-1;; (365.-low). Relative contribution 2. – of the axis to the class ;;GrpD-1;; is 635. high, then for: ;;GrpD-3;; (414.-intermediate), ;;GrpD-2;; (5.-without significance). Relative contribution 3. – of the axis to the class ;;GrpD-2;; is 1. without significance, then for: ;;GrpD-3;; (1.-without significance), ;;GrpD-1;; (0.-without significance).

* Relative contribution of the class ;;GrpD-2;; to inertia of the 1. – axis is 389., then for: ;;GrpD-3;; (186.), ;;GrpD-1;; (101.). Relative contribution of the class ;;GrpD-1;; to to inertia of the 2nd – axis is 279, then for: ;;GrpD-3;; (209.), ;;GrpD-2;; (3.). Relative contribution of the class ;;GrpD-2;; inertia 3. – axis is 1, then for: ;;GrpD-3;; (1.), ;;GrpD-1;; (0.).

*, It is inversely proportional for the class, ;;GrpD-3;;, ;;GrpD-1;;. The association of classes on the 2nd axis is proportional to the classes ;;GrpD-2;;, ;;GrpD-1;;, and inversely proportional for the classes, ;;GrpD-3;;, and inversely proportional for the classes, ;;GrpD-3;;, ;;GrpD-1;;.

Table 42 Contribution of each factor to a class in ‰:

::GrpD-1

365

635

::GrpD-2

994

::GrpD-3

585

414

* To the class ::GrpD-1 the highest contribution gives F2 factor (635 ‰:) then F1 (365‰) which contributes 1.7 times less.

Table 43 Mahalanobis distance between ;;GrpD;; in relation to anthropometric and linear hepatic measurements

::GrpD-1

::GrpD-2

::GrpD-3

::GrpD-1

.00

3.06

2.68

::GrpD-2

3.06

.00

3.34

::GrpD-3

2.68

3.34

.00

By calculating the Mahalanobis distance between ;; GrpD ;; we obtained another indicator of similarities or differences. Distances of different spaces can be compared. According to the results in the table we can say that the distance is minimal between ;;GrpD;;: ;;GrpD-3;; and ;;GrpD-1;; (::GrpD-3 and:GrpD-1 (2.68) (bigger) and the farthest are ;;GrpD;; : ;;GrpD-3;; and ;;GrpD-2;; (::GrpD-3 and:GrpD-2 (3.34) (bigger).

Table 44 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-1,::GrpD-3

2.68

::GrpD-1,::GrpD-2

3.29

From the dendrogram shown we found that the closest were groups ::GrpD-1 and GrpD-3 with the distance 2.68. The biggest difference is between ::GrpD-1 and:GrpD-2, distance 3.29.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3)

Analysis of the structure for anthropometric and linear hepatic measurements

In accordance to the previously established design of the study, it was planned to extract optimal number of factors from a sample of 98 examinees , using factor analysis of principal components, from 12 anthropometric and linear hepatic measurements: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal). The aim is to find the associations between individual variables, to determine the contribution of each factor to a variable, contribution of each variable to a factor, to apply complementary analyses and to present the results Graphically. The coordinates of the variables for anthropometric and linear hepatic measurements will be presented to determine their position in an isolated structure.

Structure of 3 isolated factors for anthropometric and linear hepatic measurements

Table 45 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

507

1000

BMI

-95

807

1000

D-il

227

402

305

1000

ApBo

122

668

687

328

1000

TvBo

215

659

611

381

801

1000

MxAp

162

297

227

202

517

353

1000

MxCo

-110

-40

163

-25

1000

MxCr

215

308

186

253

307

209

233

1000

MxCc

217

433

328

396

408

363

306

118

903

1000

Comx

211

288

178

267

197

314

621

159

232

1000

Vcal

174

341

247

341

455

351

635

489

737

750

427

1000

We found the strongest correlations (903) between Max CC (MxCc) and Maximal Crainocaudal (MxCr). The strongest negative correlation is -110 between Maximal Coronal (MxCo) and height (hgt).

Table 46 The characteristic square of a factor and the percentage contribution

sqare

sum

4.846

40.387

1.871

15.594

55.982

1.481

12.345

68.327

1.178

9.818

78.144

.936

7.804

85.948

.708

5.898

91.847

.433

3.610

95.456

.302

2.517

97.973

.158

1.314

99.287

.078

.648

99.935

.006

.051

99.986

.002

.014

100.000

Percentage representation of characteristic squares fall in the range between .014% and 40.387%. The new structure is consisted of 3 isolated factors which contain 68.327 % information from the whole sample.

Table 47 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

166

-343

118

-217

wgt

812

-789

623

129

430

185

BMI

744

-662

439

504

254

136

228

D-il

323

-557

310

-28

110

ApBo

785

-794

631

130

385

148

TvBo

759

-751

564

116

377

142

231

MxAp

363

-553

306

-237

MxCo

882

-233

-634

402

215

653

426

288

MxCr

858

-639

408

-423

179

-520

271

183

MxCc

852

-758

575

119

-340

116

-402

162

109

Comx

751

-455

207

-408

166

614

378

255

Vcal

902

-782

611

126

-526

276

148

-118

12.0

1000

The factor structure for anthropometric and linear hepatic measurements

Whole sample that consisted of 12 anthropometric and linear hepatic measurements was reduced to 3 isolated factors. Contribution of isolated factor (qlt) is significant for 9 anthropometric and linear hepatic measurements.

* The communality is higher for: liver volume (calculated by formula) (Vcal) 902, Maximal Coronal (MxCo) 882, Maximal Crainocaudal (MxCr) 858, Max CC (MxCc) 852, weight (wgt) 812, AP body dimension (ApBo) 785, Transverse body dimension (TvBo) 759, Cormax LL (Comx) 751, BMI (BMI) 744.

* Decreased communality shows that the structure of 3 isolated factors does not contain enough information about 3 anthropometric and linear hepatic measurements: Maximal Ap (MxAp) 363, Diaphragm to iliac (D-il) 323 and height (hgt) 166.

The variables that contribute in forming the structure of each isolated factor are: liver volume (calculated by formula), Maximal Coronal, Maximal Crainocaudal, Max CC, weight, AP body dimension, Transverse body dimension, Cormax LL, BMI, the variables that do not contribute to factor structure are: Maximal Ap, Diaphragm to iliac, height.

* Structure of the 1st- isolated factor is formed of 7 anthropometric and linear hepatic measurements: AP body dimension (ApBo) with factor contribution (cor) 631, weight (wgt) 623, liver volume (calculated by formula) (Vcal) 612, Max CC (MxCc) 576, Transverse body dimension (TvBo) 564, BMI (BMI) 439, Maximal Crainocaudal (MxCr) 409. Latent variables are: Diaphragm to iliac (D-il) 311, Maximal Ap (MxAp) 307. Association AP body dimension is in concordance with: weight, liver volume (calculated by formula), Max CC, Transverse body dimension, BMI, Maximal Crainocaudal, Diaphragm to iliac, Maximal Ap.

* Structure of the 2nd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: Maximal Coronal (MxCo) with factor contribution (cor) 402. Latent variables are: liver volume (calculated by formula) (Vcal) 277. Association Maximal Coronal is in concordance with: liver volume (calculated by formula).

* Structure of the 3rd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: Maximal Coronal (MxCo) with factor contribution (cor) 427. Latent variables are: Cormax LL (Comx) 378. Association Maximal Coronal is in concordance with: Cormax LL.

* Several factors contribute to variable for: Maximal Coronal, factor-2 (402), factor-3 (427), liver volume (calculated by formula), factor-1 (612), factor-2 (277).

In forming the structure of two and more factors contribute 2 anthropometric and linear hepatic measurements, in forming only one factor contribute 9 anthropometric and linear hepatic measurements, with low contribution without significance in forming the factor is 1 anthropometric and linear hepatic measurement. In forming the structure of isolated factors contribute 11 (91.67%) anthropometric and linear hepatic measurements.

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

The analysis of the sample consisting of 98 examinees revealed that in forming the structure of 3 isolated factors 50 (51.02%) had high contribution, 23 (23.47%) intermediate contribution, with low contribution without significance were 25 (25.51%).

1. – for 36 (36.73%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 10 (10.20%) examinees. For 23 we found direct proportionality, and 23 are inversely related.

2. – for 11 (11.22%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure 8 (8.16%). For 9 we found direct proportionality, and 10 are inversely related.

3. – for 10 (10.20%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure are 4 (4.08%) examinees. For 8 we found direct proportionality, and 6 examinees are inversely related.

Concordance of the anthropometric and linear hepatic measurements with the structure: two and more factor have 1 examinee, one factor have 55 examinees , latent agreement only have 15 examinees, with no agreement are 27 examinees.

It should be noted that 1 examinee stands out from the rest (inr)

Graph 17 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 18 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 19 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 20 Graphicalal representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Clustering on factors anthropometric and linear hepatic measurements

In this part of the study we clusterised 98 examinees based on 3 isolated factors from 12 variables for anthropometric and linear hepatic measurements

Sum of the levels of measures1.050

Table 49 Levels of grouping on the isolated factors

class

distance

class1

class2

nbr.elemn.

195

322

192

194

227

190

193

126

191

189

192

187

186

191

172

188

190

185

189

183

178

188

184

180

187

179

173

186

176

181

185

175

182

184

174

165

Group-1 (knot 190) contain 18 examinees, is consisted of sublevels, knots 27 and 185. The distance between them is 37. Group-2 (knot 192) contain 28 examinees, is consisted of sublevels, knots 187 and 186, the distance between them is 74. Group-3 (knot 193) contain 52 examinees, is consisted of sublevels, knots 191 and 189 and the distance between them is 127.

Mutual contributions of hierarchical classification classes and isolated factor structures for anthropometric and linear hepatic measurements

In this part of the study we analysed 11 higher classes of hierarchical classification and 3 isolated classes from the sample consisting of 98 examinees in relation to 3 isolated factors structure for the anthropometric and linear hepatic measurements. Isolated classes are: 190, 192, 193.

Centers of hierarchical classification classes and isolated factors

Table 50 Centers of 3 hierarchical classification classes in relation to 3 isolated factors structures

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qlt

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

195

192

194

1000

913

194

190

193

714

699

-194

-609

142

193

191

189

531

418

149

881

-791

177

192

187

186

286

241

253

485

1522

229

354

-43

191

172

188

173

203

303

391

-1969

276

359

478

190

185

184

300

558

-3298

555

412

-83

-198

189

183

178

357

225

173

1119

165

-219

-96

188

184

180

153

167

238

-1680

215

231

483

187

179

173

652

-1859

226

2470

399

233

648

186

176

181

214

156

359

1266

184

1206

167

-273

185

175

182

173

231

553

-2968

552

315

-160

As shown in Table 50 we found that the highest weight was 531. for the isolated class-193 This means that the biggest part of the sample which belongs to one class, belongs to this class which corresponds to the specified weighting factor, it is followed by: class-192 (286.), class-190 (184.).

* Inertia is 913 for the class-195 this means that it stands out most prominently, it is followed by: class-194 (699.), class-193 (418.), class-190 (300.), class-192 (241.), class-185 (231.), class-189 (225.), class-191 (203.), class-188 (167.), class-186 (156.), class-187 (91.).

* Contribution of isolated factors is 652, it is high, for class-187 this means that isolated factors gives the most information to this class, then for: class-190 (558.-intermediate), class-185 (553.-intermediate), class-186 (359.-low), class-191 (303.-low), class-192 (253.-without significance), class-188 (238.-without significance), class-189 (173.-without significance), class-193 (149.-without significance), class-194 (35.-without significance), class-195 (0.-without significance).

* Relative contribution of the 1st-isolated factor to the center of the class-190 is 555. intermediate, this means that factor gives the most information to this class, then for: center of the class-185 (552.-intermediate), center of the class-187 (226.-without significance), center of the class-186 (184.-without significance), center of the class-189 (165.-without significance), center of the class-193 (82.-without significance), center of the class-192 (23.-without significance), center of the class-191 (11.-without significance), center of the class-188 (4.-without significance), center of the class-194 (3.-without significance), center of the class-195 (0.-without significance). Relative contribution of the 2nd-isolated factor to the center of the class-187 is 399. low, then for: center of the class-191 (276.-low), center of the class-192 (229.-without significance), center of the class-188 (215.-without significance), center of the class-186 (167.-without significance), center of the class-193 (66.-without significance), center of the class-194 (32.-without significance), center of the class-189 (6.-without significance), center of the class-195 (0.-without significance), center of the class-190 (0.-without significance), center of the class-185 (0.-without significance). Relative contribution of the 3rd-isolated factor to the center of the class-187 is 27. without significance, then for: center of the class-188 (18.-without significance), center of the class-191 (16.-without significance), center of the class-186 (9.-without significance), center of the class-190 (2.-without significance), center of the class-185 (2.-without significance), center of the class-193 (1.-without significance), center of the class-189 (1.-without significance), center of the class-195 (0.-without significance), center of the class-194 (0.-without significance), center of the class-192 (0.-without significance).

* Association of the cluster for the 1st- factors structure is proportional between classes-195, class-190, class-195, class-192, inversely proportional with, class-193, class-192, class-191, class-189, class-188, class-186.

* Association of the cluster for the 2nd- factors structure is proportional between classes-195, class-193, class-190, class-185, class-193, class-189, inversely proportional with, class-192, class-187, class-186, class-185.

* Association of the cluster for the 3rd- factors structure is proportional between classes-195, class-193, class-190, class-189, class-195, inversely proportional with, class-192, class-190, class-189, class-186, class-185.

Table 51 Center of hierarchical classification classes in relation to the factors axis 1 (factor variance: 4.8465)

knot

knot1

knot2

weight

inr

dst

(F1)2

acor

cor

ctr

cos

+cos2

195

192

194

1000

913

10950

194

190

193

714

699

11737

-194

-57

193

191

189

531

418

9446

881

776

412

287

192

187

186

286

241

10113

485

235

152

191

172

188

173

203

14032

391

153

104

190

185

184

300

19590

-3298

10877

1998

555

412

-745

555

189

183

178

357

225

7573

1119

1252

447

165

407

165

188

184

180

153

167

13098

238

187

179

173

15298

-1859

3456

247

226

-475

226

186

176

181

214

156

8729

1266

1602

343

184

429

184

185

175

182

173

231

15958

-2968

8807

1528

552

315

-743

552

As shown in Table 51 the greatest distance (dst) 19590. between the center of the cloud and the center of the class-190, it is followed by: class-185 (15958.), class-187 (15298.), class-191 (14032.), class-188 (13098.), class-194 (11737.), class-195 (10950.), class-192 (10113.), class-193 (9446.), class-186 (8729.), class-189 (7573.).

* Absolute contribution (acor) is 1998 for the class-190, followed by absolute contribution for: class-185 (1528.), class-189 (447.), class-193 (412.), class-186 (343.), class-187 (247.), class-192 (67.), class-194 (27.), class-191 (26.), class-188 (9.), class-195 (0.).

* The cosine of an angle (cos) -745. between the radius of the center of the class -190 and axis, class-185 (-743.), class-187 (-475.), class-186 (429.), class-189 (407.), class-193 (287.), class-192 (152.), class-191 (104.), class-188 (66.), class-194 (-57.), class-195 (0.).

Table 52 Center of hierarchical classification classes in relation to the factors axis 2 (factor variance: 1.8713)

knot

knot1

knot2

weight

inr

dst

(F2)2

acor

cor

ctr

cos

+cos2

195

192

194

1000

913

10950

194

190

193

714

699

11737

-609

371

265

142

-178

193

191

189

531

418

9446

-791

625

332

177

-257

148

192

187

186

286

241

10113

1522

2317

662

229

354

479

252

191

172

188

173

203

14032

-1969

3876

672

276

359

-526

287

190

185

184

300

19590

-83

-19

556

189

183

178

357

225

7573

-219

-80

172

188

184

180

153

167

13098

-1680

2822

432

215

231

-464

220

187

179

173

15298

2470

6100

436

399

233

632

625

186

176

181

214

156

8729

1206

1455

312

167

408

350

185

175

182

173

231

15958

552

* Absolute contribution (acor) is 672 for the class-191 followed by absolute contribution for: class-192 (662.), class-187 (436.), class-188 (432.), class-193 (332.), class-186 (312.), class-194 (265.), class-189 (17.), class-190 (1.), class-195 (0.), class-185 (0.).

* The cosine of an angle (cos) 632. between the radius of the center of the class -187 and axis, class-191 (-526.), class-192 (479.), class-188 (-464.), class-186 (408.), class-193 (-257.), class-194 (-178.), class-189 (-80.), class-190 (-19.), class-185 (1.), class-195 (0.).

Table 53 Center of hierarchical classification classes in relation to the factors axis 3 (factor variance: 1.4814)

knot

knot1

knot2

weight

inr

dst

(F3)2

acor

cor

ctr

cos

+cos2

195

192

194

1000

913

10950

194

190

193

714

699

11737

193

191

189

531

418

9446

149

192

187

186

286

241

10113

-43

-14

253

191

172

188

173

203

14032

478

228

128

303

190

185

184

300

19590

-198

-45

558

189

183

178

357

225

7573

-96

-35

173

188

184

180

153

167

13098

483

234

134

238

187

179

173

15298

648

420

166

652

186

176

181

214

156

8729

-273

-93

359

185

175

182

173

231

15958

-160

-40

553

* Absolute contribution (acor) 40. class-191 followed by absolute contribution for: class-188 (36.), class-187 (30.), class-186 (16.), class-190 (7.), class-193 (4.), class-185 (4.), class-189 (3.), class-192 (1.), class-195 (0.), class-194 (0.).

* The cosine of an angle (cos) 166. between the radius of the center of the class -187 and the axis, class-188 (134.), class-191 (128.), class-186 (-93.), class-190 (-45.), class-185 (-40.), class-189 (-35.), class-193 (30.), class-192 (-14.), class-194 (5.), class-195 (0.).

Analysis of differences between two nodes (dipoles) of hierarchical classification classes

Table 54 Dipoles of the 11 highest nodes in relation to the factors axes from 1 to 3

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qld

cod

ctd

cod

ctd

cod

ctd

195

192

194

1000

3169

678

291

2131

2875

495

-60

194

190

193

714

10837

-4179

10486

492

708

301

-289

193

191

189

531

3618

-728

489

-1750

2825

191

574

304

192

187

186

286

8864

-3125

7088

108

1263

1159

922

617

191

172

188

173

3525

1298

770

-2455

2754

-48

190

185

184

9888

-5948

9124

-1581

645

-679

119

189

183

178

357

10887

2129

10292

392

350

329

246

188

184

180

153

10981

3034

10384

538

326

-489

270

187

179

173

3828

-1357

907

2351

2720

640

202

186

176

181

214

4846

-857

2394

-848

2344

-181

107

185

175

182

173

10280

-1500

5557

-791

1546

-1134

3178

As shown in Table 54 we found that Inertia of the dipole (ind) a(n) b(n) is 27, that is, the inertia of the whole system, class-195, followed by dipoles: class-194 (19.), class-193 (11.), class-192 (6.), class-191 (3.), class-190 (3.), class-189 (3.), class-188 (3.), class-187 (2.), class-186 (1.), class-185 (1.).

* The quality of the observed factors (qld) 10981. is high, for class-188 (dipole) which represents the quality of the vector ab representation in the factors space of this research, the other qualities are for: class-189 (10887.-high), class-194 (10837.-high), class-185 (10280.-high), class-190 (9888.-high), class-192 (8864.-high), class-186 (4846.-high), class-187 (3828.-high), class-193 (3618.-high), class-191 (3525.-high), class-195 (3169.-high).

* Projection ab on the axis 1st-isolated factor, that is, the projection of the dipole class-190 is -5948, other dipole projections on the axis are: class-194 (-4179.), class-192 (-3125.), class-188 (3034.), class-189 (2129.), class-185 (-1500.), class-187 (-1357.), class-191 (1298.), class-186 (-857.), class-193 (-728.), class-195 (678.). Projection ab on the axis 2nd-isolated factor, that is, the projection of the dipole class-191 is -2455, other dipole projections on the axis are: class-187 (2351.), class-195 (2131.), class-193 (-1750.), class-190 (-1581.), class-192 (1263.), class-186 (-848.), class-185 (-791.), class-194 (708.), class-188 (538.), class-189 (392.). Projection ab on the axis 3rd-isolated factor, that is, the projection of the dipole class-185 is -1134, other dipole projections on the axis are: class-192 (922.), class-190 (-679.), class-187 (640.), class-193 (574.), class-188 (-489.), class-189 (329.), class-194 (-289.), class-186 (-181.), class-195 (-60.), class-191 (-48.).

* Relative contribution of the 1st-factor axis (D1), dipole a(n) b(n) is class-194 is 10486. which is high, it represents the angle between the axis of the vector factor ab (dipole) other angles for: class-188 (10384.-high), class-189 (10292.-high), class-190 (9124.-high), class-192 (7088.-high), class-185 (5557.-high), class-186 (2394.-high), class-187 (907.-high), class-191 (770.-high), class-193 (489.-intermediate), class-195 (291.-low). Relative contribution of the 2nd-factor axis (D2), dipole a(n) b(n) is class-195 is 2875. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-193 (2825.-high), class-191 (2754.-high), class-187 (2720.-high), class-186 (2344.-high), class-185 (1546.-high), class-192 (1159.-high), class-190 (645.-high), class-189 (350.-low), class-188 (326.-low), class-194 (301.-low). Relative contribution of the 3rd-factor axis (D3), dipole a(n) b(n) is class-185 is 3178. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-192 (617.-high), class-193 (304.-low), class-188 (270.-without significance), class-189 (246.-without significance), class-187 (202.-without significance), class-190 (119.-without significance), class-186 (107.-without significance), class-194 (50.-without significance), class-195 (2.-without significance), class-191 (1.-without significance).

* Relative contribution of dipoles (ctd) class-194 to axis of the 1st-factor is 10486, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-192 (7088.), class-189 (10292.), class-190 (9124.), class-188 (10384.), class-195 (291.), class-185 (5557.), class-193 (489.), class-186 (2394.), class-191 (770.), class-187 (907.). Relative contribution of dipoles (ctd) class-195 to axis of the 2nd-factor is 2875, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-193 (2825.), class-191 (2754.), class-192 (1159.), class-187 (2720.), class-194 (301.), class-186 (2344.), class-190 (645.), class-185 (1546.), class-189 (350.), class-188 (326.). Relative contribution of dipoles (ctd) class-192 to axis of the 3rd-factor is 617, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-185 (3178.), class-193 (304.), class-194 (50.), class-189 (246.), class-188 (270.), class-187 (202.), class-190 (119.), class-186 (107.), class-195 (2.), class-191 (1.).

Table 55 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 1

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

195

192

194

204

322

678

460

291

540

291

194

190

193

136

318

-4179

17462

2383

10486

492

-3238

10486

193

191

189

117

239

-728

530

489

-699

489

192

187

186

258

-3125

9764

523

7088

108

-2662

7088

191

172

188

227

1298

1685

770

877

770

190

185

203

-5948

35384

341

9124

-3021

9124

189

183

178

103

2129

4531

378

10292

3208

10292

188

184

180

213

3034

9204

338

10384

3222

10384

187

179

173

415

-1357

1842

907

-952

907

186

176

181

-857

734

2394

-1547

2394

185

175

182

-1500

2249

5557

-2357

5557

As shown in Table 55 the greatest distance (dst) 415. between the center of the cloud and the center of the class-187, it is followed by: class-195 (322.), class-194 (318.), class-192 (258.), class-193 (239.), class-191 (227.), class-188 (213.), class-190 (203.), class-189 (103.), class-185 (84.), class-186 (68.).

* Absolute contribution (acor) 2383. Class is 194 followed by absolute contribution for: class-192 (523.), class-189 (378.), class-190 (341.), class-188 (338.), class-195 (94.), class-185 (81.), class-193 (62.), class-186 (35.), class-191 (30.), class-187 (27.).

* The cosine of an angle (cos) -3238. between the radius of the center of the class -194 and axis, class-188 (3222.), class-189 (3208.), class-190 (-3021.), class-192 (-2662.), class-185 (-2357.), class-186 (-1547.), class-187 (-952.), class-191 (877.), class-193 (-699.), class-195 (540.).

Table 56 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 2

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

195

192

194

204

322

2131

4541

927

2875

495

1696

3167

194

190

193

136

318

708

501

301

548

10786

193

191

189

117

239

-1750

3063

358

2825

191

-1681

3315

192

187

186

258

1263

1596

1159

1076

8247

191

172

188

227

-2455

6028

109

2754

-1660

3524

190

185

203

-1581

2500

645

-803

9769

189

183

178

103

392

154

350

591

10641

188

184

180

213

538

289

326

571

10711

187

179

173

415

2351

5526

2720

1649

3626

186

176

181

-848

719

2344

-1531

4738

185

175

182

-791

626

1546

-1243

7102

* Absolute contribution (acor) is 2383. For the class-194 followed by absolute contribution for: class-192 (523.), class-189 (378.), class-190 (341.), class-188 (338.), class-195 (94.), class-185 (81.), class-193 (62.), class-186 (35.), class-191 (30.), class-187 (27.).

Table 57 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 3

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

195

192

194

204

322

-60

-48

3169

194

190

193

136

318

-289

-224

10837

193

191

189

117

239

574

329

304

551

3618

192

187

186

258

922

849

617

785

8864

191

172

188

227

-48

-33

3525

190

185

203

-679

461

119

-345

9888

189

183

178

103

329

108

246

496

10887

188

184

180

213

-489

239

270

-520

10981

187

179

173

415

640

410

202

449

3828

186

176

181

-181

107

-327

4846

185

175

182

-1134

1286

3178

-1783

10280

* Absolute contribution (acor) 2383. class-194 followed by absolute contribution for: class-192 (523.), class-189 (378.), class-190 (341.), class-188 (338.), class-195 (94.), class-185 (81.), class-193 (62.), class-186 (35.), class-191 (30.), class-187 (27.).

Table 58 Relative mutual contributions of factors (from 1 to 3) per classes

kls

knot1

knot2

Q(n)

inr

+inr

195

192

194

204

194

190

193

136

199

193

191

189

117

192

187

186

191

172

188

190

185

189

183

178

188

184

180

187

179

173

186

176

181

185

175

182

Significance of dipole association coefficient (class) Q(n) is the highest for the class-195 (204.), followed by: class-194 (136.), class-193 (117.), class-189 (83.), class-192 (54.), class-186 (48.), class-188 (37.), class-185 (36.), class-191 (18.), class-187 (15.), class-190 (10.).

* Inertia is 27 for the class-195 this means that it stands out most prominently, it is followed by: class-194 (19.), class-193 (11.), class-192 (6.), class-191 (3.), class-190 (3.), class-189 (3.), class-188 (3.), class-187 (2.), class-186 (1.), class-185 (1.).

* The contribution of the 1st- isolated factor to the class-194 is 199, this means that examinees who belong to the class-194 have anthropometric and linear hepatic characteristics of the 1st-factors structure, followed by: class-192 (44.), class-189 (31.), class-190 (28.), class-188 (28.), class-195 (8.), class-185 (7.), class-193 (5.), class-191 (3.), class-186 (3.), class-187 (2.). The contribution of the 2nd- isolated factor to the class-195 is 77. followed by: class-193 (30.), class-191 (9.), class-192 (7.), class-187 (7.), class-194 (6.), class-186 (3.), class-190 (2.), class-185 (2.), class-189 (1.), class-188 (1.). The contribution of the 3rd- isolated factor to the class-192 is 4. followed by: class-185 (4.), class-193 (3.), class-194 (1.), class-189 (1.), class-188 (1.), class-195 (0.), class-191 (0.), class-190 (0.), class-187 (0.), class-186 (0.).

The greatest contribution of a factor to the class -195 (77.) gives the 1st- factor, This means that mentioned structure have examinees of the observed class.

*The highest contribution of the factor to the class-195 (77.) has the 1st- factor, this means that mentioned structure have examinees of the observed class. The same can be said, with less contribution for characteristics of the factor-2 (8.), factor-3 (0.). The contribution to the class-194 (199.) belongs to 1.- factor and factor-2 (6.), factor-3 (1.). The contribution to the class-193 (30.) belongs to 1.- factor and factor-2 (5.), factor-3 (3.). The contribution to the class-192 (44.) belongs to 1.- factor and factor-2 (7.), factor-3 (4.). The contribution to the class-191 (9.) belongs to 1.- factor and factor-2 (3.), factor-3 (0.). The contribution to the class-190 (28.) belongs to 1.- factor and factor-2 (2.), factor-3 (0.). The contribution to the class-189 (31.) belongs to 1.- factor and factor-2 (1.), factor-3 (1.). The contribution to the class-188 (28.) belongs to 1.- factor and factor-2 (1.), factor-3 (1.). The contribution to the class-187 (7.) belongs to 1.- factor and factor-2 (2.), factor-3 (0.). The contribution to the class-186 (3.) belongs to 1.- factor and factor-2 (3.), factor-3 (0.). The contribution to the class-185 (7.) belongs to 1.- factor and factor-2 (4.), factor-3 (2.).

Presentation of isolated classes

Significance of dipole association coefficient (class) Q(n) is the highest for the class-193 (117.) followed by: class-192 (54.), class-190 (10.).

* Inertia of the 11th class-193 this means that it stands out most prominently, it is followed by: class-192 (6.), class-190 (3.).

* The contribution of the 1st- isolated factor to the class-192 is 44. followed by: class-190 (28.), class-193 (5.). The contribution of the 2nd- isolated factor to the class-193 is 30. followed by: class-192 (7.), class-190 (2.). The contribution of the 3rd- isolated factor to the class-192 is 4. followed by: class-193 (3.), class-190 (0.).

*, factor-3 (0.), factor-3 (1.), factor-3 (3.), factor-3 (4.), factor-3 (0.), factor-3 (0.), factor-3 (1.), factor-3 (1.), factor-3 (0.), factor-3 (0.), factor-2 (4.).

Structure of 3 isolated factors for anthropometric and linear hepatic measurements

Table 59 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

507

1000

BMI

-95

807

1000

D-il

227

402

305

1000

ApBo

122

668

687

328

1000

TvBo

215

659

611

381

801

1000

MxAp

162

297

227

202

517

353

1000

MxCo

-110

-40

163

-25

1000

MxCr

215

308

186

253

307

209

233

1000

MxCc

217

433

328

396

408

363

306

118

903

1000

Comx

211

288

178

267

197

314

621

159

232

1000

Vcal

174

341

247

341

455

351

635

489

737

750

427

1000

We found the strongest correlations (903) between Max CC (MxCc) and Maximal Crainocaudal (MxCr). The strongest negative correlation is -110 between Maximal Coronal (MxCo) and height (hgt).

Table 60 The characteristic square of a factor and the percentage contribution

sqare

sum

4.846

40.387

1.871

15.594

55.982

1.481

12.345

68.327

1.178

9.818

78.144

.936

7.804

85.948

.708

5.898

91.847

.433

3.610

95.456

.302

2.517

97.973

.158

1.314

99.287

.078

.648

99.935

.006

.051

99.986

.002

.014

100.000

Percentage representation of the characteristic squares fall in the range between .014% and 40.387%. The new structure is consisted of 3 isolated factors which contain 68.327 % information from the whole sample.

Table 61 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

166

-343

118

-217

wgt

812

-789

623

129

430

185

BMI

744

-662

439

504

254

136

228

D-il

323

-557

310

-28

110

ApBo

785

-794

631

130

385

148

TvBo

759

-751

564

116

377

142

231

MxAp

363

-553

306

-237

MxCo

882

-233

-634

402

215

653

426

288

MxCr

858

-639

408

-423

179

-520

271

183

MxCc

852

-758

575

119

-340

116

-402

162

109

Comx

751

-455

207

-408

166

614

378

255

Vcal

902

-782

611

126

-526

276

148

-118

12.0

1000

The isolated factors structure for anthropometric and linear hepatic measurements

* Several factors contribute to variable for: Maximal Coronal, factor-2 (402), factor-3 (427), liver volume (calculated by formula), factor-1 (612), factor-2 (277).

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

The analysis of the sample consisting of 98 examinees revealed that in forming the structure of 3 isolated factors 50 (51.02%) examinees have high contribution, 23 (23.47%) examinees have intermediate contribution, with low contribution, without significance are 25 (25.51%).

2. – for 11 (11.22%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure are 8 (8.16%) examinees. For 9 we found direct proportionality, and 10 examinees were inversely related.

3. – for 10 (10.20%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure are 4 (4.08%). For 8 examinees we found direct proportionality, and were inversely related.

Concordance of anthropometric and linear hepatic measurements with the structure: two and more factor have 1 examinee, one factor have 55 examinees, latent agreement only have 15 examinees, with no agreement are 27 examinees.

It should be noted that 1 examinee stands out from the rest (inr)

Graph 21 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 22 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 23 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 24 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Table 62 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-2,::GrpD-0

.05

::GrpD-3,::GrpD-0

.15

::GrpD-0,::GrpD-0

.19

::GrpD-1,::GrpD-0

.21

::GrpD-2,::GrpD-3

.27

::GrpD-0,::GrpD-0

.32

::GrpD-1,::GrpD-0

.42

::GrpD-0,::GrpD-0

.45

::GrpD-1,::GrpD-0

1.09

::GrpD-1,::GrpD-0

1.90

::GrpD-1,::GrpD-2

2.10

From the dendrogram shown we found that the closest were groups ::GrpD-2 and:GrpD-0 with the distance 0.05.The biggest difference is between::GrpD-1 and:GrpD-2, distance 2.10.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3) ;;GrpD-0;; (4) ;;GrpD-0;; (5) ;;GrpD-0;; (6) ;;GrpD-0;; (7) ;;GrpD-0;; (8) ;;GrpD-0;; (9) ;;GrpD-0;; (10) ;;GrpD-0;; (11) ;;GrpD-0;; (12)

The mutual contribution of the division classes and factors structure for anthropometric and linear hepatic measurements

Table 63 Mutual contributions among division groups (3) and isolated factors structure

1-factor

2-factor

3-factor

weight

inr

kvl

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

::GrpD-1

184

167

1000

-3298

996

412

-83

-198

::GrpD-2

286

1000

485

1522

907

354

-43

::GrpD-3

531

1000

881

550

-791

444

177

As shown in Table 63 we found that the highest weight was 531. for the class ;;GrpD-3;; This means that the biggest part of the sample which belongs to one class, belongs to this class which corresponds to the specified weighting factor, and the next is for the class: ;;GrpD-2;; (286.), ;;GrpD-1;; (184.).

* Inertia (inr) of the class ;;GrpD-1;; is 167 it means that this class stands out from the rest, and the next is for class: ;;GrpD-3;; (62.), ;;GrpD-2;; (61.).

* Relative contribution (cor) 1. – of the axis to the class ;;GrpD-1;; is 996- high, which means that the axis has the most information about that class, then for: ;;GrpD-3;; (550.-intermediate), ;;GrpD-2;; (92.-without significance). Relative contribution 2. – of the axis to the class ;;GrpD-2;; is 907- high, then for: ;;GrpD-3;; (444.-intermediate), ;;GrpD-1;; (1.-without significance). Relative contribution 3. – of the axis to the class ;;GrpD-3;; is 6. without significance, then for: ;;GrpD-1;; (4.-without significance), ;;GrpD-2;; (1.-without significance).

* Relative contribution of the class ;;GrpD-1;; to inertia of the 1st – axis is 412., then for: ;;GrpD-3;; (85.), ;;GrpD-2;; (14.). Relative contribution of the class ;;GrpD-2;; to inertia of the 2nd – axis is 354, then for: ;;GrpD-3;; (177.), ;;GrpD-1;; (1.). Relative contribution of the class ;;GrpD-1;; to inertia of the 3rd – axis is 5, then for: ;;GrpD-3;; (3.), ;;GrpD-2;; (0.).

* The association of classes on the 2nd axis is proportional for the classes ;;GrpD-1;;, and ;;GrpD-3;;, and inversely proportional for the class, ;;GrpD-2;;. Association of classes on the 3rd – axis is proportional for classes ;;GrpD-1;;, ;;GrpD-2;;, and inversely proportional for the class, ;;GrpD-3;;.

Table 64 Contribution of each factor to a class in ‰:

::GrpD-1

996

::GrpD-2

907

::GrpD-3

550

444

* The factor F1 gives the highest contribution to the class ::GrpD-1 (996 :‰:) then F3 (4‰) which contributes 249.0 times less. To a class ::GrpD-2 the highest contribution gives factor F2 (907 :‰:) then F1 (92‰) which contributes 9.9 times less. To a class ::GrpD-3 the highest contribution gives F1 factor (550 :‰:) then F2 (444‰) which contributes 1.2 times less.

Table 65 Class and inertia of the factors axis-absolute contribution

mass

dcnt

actr1

actr2

actr3

::GrpD-1

184

10923

2001

::GrpD-2

286

2553

662

::GrpD-3

531

1409

412

332

* Distance between center of the class and the cloud center (dcnt) is the biggest for the class::GrpD-1 (10923), this means that this class stands out the most from the others followed by: class ::GrpD-2 (2553) and class ::GrpD-3 (1409).

* Absolute contribution of the class ::GrpD-1 to inertia of the 1st- axis (2001), this means mass *distance squared followed by: class ::GrpD-3 (412), class ::GrpD-2 (67). Absolute contribution of the class ::GrpD-2 to inertia of the 2nd axis (662), this means mass *distance squared followed by: class ::GrpD-3 (332), class ::GrpD-1 (1). Absolute contribution of the class ::GrpD-1 to inertia of the 3rd axis (7), this means mass *distance squared followed by: class ::GrpD-3 (4), class ::GrpD-2 (0). The highest absolute contribution of the class ::GrpD-1 to inertia of the axis is for the 1st- axis (2001) then for the 2nd- axis (1). The highest absolute contribution of the class ::GrpD-2 to inertia of the axis is for the 2nd- axis (662) then for the 3rd- axis (0). The highest absolute contribution of the class ::GrpD-3 to inertia of the axis is for the 1st- axis (412) then for the 3rd- axis (4).

Table 66 Mutual contributions of the the isolated factors structures and differences between two centers of the groups (dipoles)

1-factor

2-factor

3-factor

Group

inr

kvl

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

1890

1000

3783

846

330

1605

152

154

155

2462

1000

4179

968

492

-708

289

1026

1000

396

-2313

968

531

134

Table 67 Mahalanobis distance between ;;GrpD;; in relation to anthropometric and linear hepatic measurements

::GrpD-1

::GrpD-2

::GrpD-3

::GrpD-1

.00

2.86

2.88

::GrpD-2

2.86

.00

2.49

::GrpD-3

2.88

2.49

.00

By calculating the Mahalanobis distance between ;; GrpD ;; we obtained another indicator of similarities or differences. Distances of different spaces can be compared. According to the results in the table we can say that the distance is minimal between ;;GrpD;;: ;;GrpD-3;; and ;;GrpD-2;; (::GrpD-3 and:GrpD-2 (2.49) (bigger) . The farthest are ;;GrpD;; : ;;GrpD-3;; and ;;GrpD-1;; (::GrpD-3 and:GrpD-1 (2.88) (bigger).

Table 68 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-2,::GrpD-3

2.49

::GrpD-1,::GrpD-2

2.97

From the dendrogram shown we found that the closest were groups ::GrpD-2 and:GrpD-3 with the distance 2.49.The biggest difference is between::GrpD-1 and:GrpD-2 with the distance 2.97.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3)

Analysis of the structure for anthropometric and linear hepatic measurements

In accordance to the previously established design of the study, it was planned to extract optimal number of factors from the sample of 58 examinees, using factor analysis of principal components using 12 anthropometric and linear hepatic measurements: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal). The aim is to find the associations between individual variables and to determine the contribution of each factor to a variable, contribution of each variable to a factor, to apply complementary analyses and to present the results Graphically. The coordinates of the variables for anthropometric and linear hepatic measurements will be presented to determine their position in an isolated structure.

Structure of 3 isolated factors anthropometric and linear hepatic measurements

Table 69 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

263

1000

BMI

-308

834

1000

D-il

-12

347

322

1000

ApBo

-50

709

729

228

1000

TvBo

712

644

267

865

1000

MxAp

619

580

423

714

647

1000

MxCo

237

161

167

-81

1000

MxCr

-90

-25

-12

1000

MxCc

-69

136

194

225

114

136

921

1000

Comx

197

183

239

140

182

868

-82

1000

Vcal

117

502

432

400

492

414

536

610

497

595

543

1000

We found the strongest correlations (921) between Max CC (MxCc) and Maximal Crainocaudal (MxCr) . The strongest negative correlation is -308 between BMI (BMI) and height (hgt).

Table 70 The characteristic square of a factor and the percentage contribution

sqare

sum

4.625

38.543

2.246

18.713

57.255

2.027

16.892

74.148

1.070

8.917

83.065

.852

7.104

90.169

.512

4.266

94.435

.381

3.172

97.608

.118

.987

98.595

.106

.886

99.481

.055

.459

99.940

.006

.048

99.988

.001

.012

100.000

Percentage representation of the characteristic squares fall in the range between .012% and 38.543%. The new structure is consisted of 3 isolated factors which contain 74.148 % information from the whole sample.

Table 71 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

225

-61

301

-362

131

wgt

789

-849

722

156

-178

-188

BMI

761

-802

643

139

-341

116

D-il

263

-488

239

-135

ApBo

823

-854

730

158

-304

-19

TvBo

764

-810

656

142

-295

-145

MxAp

703

-769

591

128

-327

107

-72

MxCo

904

-281

827

684

305

-376

141

MxCr

946

-252

337

113

877

769

380

MxCc

945

-389

151

345

119

821

674

333

Comx

851

-351

123

724

524

233

-451

203

100

Vcal

924

-790

623

135

524

274

122

163

12.0

1000

The factor structure of anthropometric and linear hepatic measurements

* The communality is higher for: Maximal Crainocaudal (MxCr) 946, Max CC (MxCc) 945, liver volume (calculated by formula) (Vcal) 924, Maximal Coronal (MxCo) 904, Cormax LL (Comx) 851, AP body dimension (ApBo) 823, weight (wgt) 789, Transverse body dimension (TvBo) 764, BMI (BMI) 761, Maximal Ap (MxAp) 703.

The variables that contribute in forming the structure of each isolated factor are: Maximal Crainocaudal, Max CC, liver volume (calculated by formula), Maximal Coronal, Cormax LL, AP body dimension, weight, Transverse body dimension, BMI, Maximal Ap, the variables that do not contribute to factor structure are: Diaphragm to iliac, height.

* Structure of the 1st- isolated factor is formed of 6 anthropometric and linear hepatic measurements: AP body dimension (ApBo) with factor contribution (cor) 731, weight (wgt) 722, Transverse body dimension (TvBo) 657, BMI (BMI) 644, liver volume (calculated by formula) (Vcal) 624, Maximal Ap (MxAp) 591. Association AP body dimension is in concordance with: weight, Transverse body dimension, BMI, liver volume (calculated by formula), Maximal Ap.

* Structure of the 2nd- isolated factor is formed of 2 anthropometric and linear hepatic measurements: Maximal Coronal (MxCo) with factor contribution (cor) 684, Cormax LL (Comx) 524. Latent variables are: liver volume (calculated by formula) (Vcal) 275. Association Maximal Coronal is in concordance with: Cormax LL, liver volume (calculated by formula).

* Structure of the 3rd- isolated factor is formed of 2 anthropometric and linear hepatic measurements: Maximal Crainocaudal (MxCr) with factor contribution (cor) 770, Max CC (MxCc) 675. Association Maximal Crainocaudal is in concordance with: Max CC.

* Several factors contribute to variable for: liver volume (calculated by formula), factor-1 (624), factor-2 (275).

In forming the structure of two and more factors contribute 1 anthropometric and linear hepatic measurement, in forming only one factor contribute 9 anthropometric and linear hepatic measurements, with low contribution without significance in forming the factor is 2 anthropometric and linear hepatic measurements. In forming the structure of isolated factors contribute 10 (83.33%) anthropometric and linear hepatic measurements.

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

Revealed that in forming the structure of 3 isolated factors (from the sample of 58 examinees) 40 (68.97%) examinees have high contribution, 8 (13.79%) examinees have intermediate contribution, with low contribution, without significance are 10 (17.24%).

1. – for 22 (37.93%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 4 (6.90%) examinees. For 11 examinees we found direct proportionality, and 15 are inversely related.

2. – for 9 (15.52%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure are 6 (10.34%) examinees. For 9 examinees we found direct proportionality, and for 6 are inversely related.

3. – for 7 (12.07%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure are 10 (17.24%) examinees. For 8 examinees we found direct proportionality, and 9 are inversely related.

Concordance of anthropometric and linear hepatic measurements with the structure: two and more factor have 2 examinees , one factor have 34 examinees , latent agreement only have 13 examinees, with no agreement are 9 .

It should be noted that 3 examinees stand out from the rest (inr)

Graph 25 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 26 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 27 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 28 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Clustering on factors anthropometric and linear hepatic measurements

In this part of the study we clusterised 135 examinees based on 3 isolated factors from 12 variables of anthropometric and linear hepatic measurements

Sum of the levels of measures is 1.269

Table 115 Levels of grouping on the isolated factors

class

distance

class1

class2

nbr.elemn.

269

399

265

268

135

268

298

262

267

105

267

168

266

263

266

264

259

265

260

257

264

258

252

263

232

261

262

253

244

261

251

250

260

248

256

259

249

255

258

254

243

Group-1 (knot 262) contain 21 examinees, is consisted of sublevels, knots 253 and 244 and distance between them is 22. Group-2 (knot 265) contain 30 examinees is consisted of sublevels, knots 260 and 257, distance between them is 62. Group-3 (knot 267) contain 84 examinees, is consisted of sublevels, knots 266 and 263 and distance between them is 168.

Mutual contributions of hierarchical classification classes and isolated factor structures for anthropometric and linear hepatic measurements

In this part of the study we analysed 11 higher classes of hierarchical classification and 3 isolated classes from the sample consisting of 135 examinees in relation to 3 isolated factors structure for the anthropometric and linear hepatic measurements. Isolated classes are: 262, 265, 267.

Centers of hierarchical classification classes and isolated factors

Table 116 Centers of 3 hierarchical classification classes in relation to 3 isolated factors structures

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qlt

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

269

265

268

1000

894

268

262

267

778

612

278

567

126

-33

267

266

263

622

419

175

1106

151

159

434

266

264

259

422

251

140

421

887

110

168

183

265

260

257

222

315

287

-974

-1984

231

442

115

264

258

252

193

146

482

1521

254

1397

214

190

353

263

232

261

200

182

630

2552

596

273

-523

-318

262

253

244

156

218

622

-3031

547

299

1098

-251

261

251

250

163

141

601

2454

579

206

-239

-409

260

248

256

104

218

376

-2495

247

135

-1784

126

167

215

259

249

255

230

112

-502

459

As shown in Table 116 we found that the highest weight was 622. for isolated class-267 This means that the biggest part of the sample which belongs to one class, belongs to this class which corresponds to the specified weighting factor, it is followed by: class-265 (222.), class-262 (156.).

* Inertia is 894 for the class-269 this means that it stands out most prominently, it is followed by: class-268 (612.), class-267 (419.), class-265 (315.), class-266 (251.), class-262 (218.), class-260 (218.), class-263 (182.), class-264 (146.), class-261 (141.), class-259 (112.).

* Contribution of isolated factors 630. is high, for class-263 this means that isolated factors gives the most information to this class, then for: class-262 (622.-high), class-261 (601.-high), class-264 (482.-intermediate), class-260 (376.-low), class-265 (287.-low), class-267 (175.-without significance), class-266 (140.-without significance), class-259 (79.-without significance), class-268 (42.-without significance), class-269 (0.-without significance).

* Relative contribution of the 1st-isolated factor to the center of the class-263 is 596. intermediate, this means that the factor give the most information to this class, then for: the center of the class-261 (579.-intermediate), center of the class-262 (547.-intermediate), center of the class-264 (254.-without significance), center of the class-260 (247.-without significance), center of the class-267 (151.-without significance), center of the class-265 (56.-without significance), center of the class-259 (43.-without significance), center of the class-266 (25.-without significance), center of the class-268 (8.-without significance), center of the class-269 (0.-without significance). Relative contribution of the 2nd-isolated factor to the center of the class-265 is 231. without significance, then for: center of the class-264 (214.-without significance), center of the class-260 (126.-without significance), center of the class-266 (110.-without significance), center of the class-262 (72.-without significance), center of the class-259 (36.-without significance), center of the class-268 (34.-without significance), center of the class-263 (25.-without significance), center of the class-267 (23.-without significance), center of the class-261 (5.-without significance), center of the class-269 (0.-without significance). Relative contribution of the 3rd-isolated factor to the center of the class-261 is 16. without significance, then for: center of the class-264 (14.-without significance), center of the class-263 (9.-without significance), center of the class-266 (5.-without significance), center of the class-262 (4.-without significance), center of the class-260 (2.-without significance), center of the class-265 (1.-without significance), center of the class-269 (0.-without significance), center of the class-268 (0.-without significance), center of the class-267 (0.-without significance), center of the class-259 (0.-without significance).

* Association of the cluster for the 1st- factors structure is proportional between classes-269, class-267, class-266, class-260, class-265, class-268, inversely proportional with, class-265, class-262, class-260, class-259.

* Association of the cluster for the 2nd- factors structure is proportional between classes-269, class-267, class-266, class-260, class-269, class-259, inversely proportional with, class-265, class-263, class-261, class-260.

* Association of the cluster for the 3rd- factors structure is proportional between classes-269, class-263, class-269, class-268, inversely proportional with, class-267, class-266, class-265, class-264, class-260, class-259.

Table 117 Center of hierarchical classification classes in relation to the factors axis 1 (factor variance: 4.7745)

knot

knot1

knot2

weight

inr

dst

(F1)2

acor

cor

ctr

cos

+cos2

269

265

268

1000

894

10731

268

262

267

778

612

9445

278

267

266

263

622

419

8085

1106

1222

761

151

159

389

151

266

264

259

422

251

7139

421

177

158

265

260

257

222

315

17032

-974

948

211

-236

264

258

252

193

146

9100

1521

2313

446

254

504

254

263

232

261

200

182

10926

2552

6510

1302

596

273

772

596

262

253

244

156

218

16800

-3031

9188

1429

547

299

-740

547

261

251

250

163

141

10400

2454

6022

981

579

206

761

579

260

248

256

104

218

25172

-2495

6227

646

247

135

-497

247

259

249

255

230

112

5870

-502

252

-207

As shown in Table 117 the greatest distance (dst) 25172. between the center of the cloud and the center of the class-260, it is followed by: class-265 (17032.), class-262 (16800.), class-263 (10926.), class-269 (10731.), class-261 (10400.), class-268 (9445.), class-264 (9100.), class-267 (8085.), class-266 (7139.), class-259 (5870.).

* Absolute contribution (acor) is 1429. class-262 followed by absolute contribution for: class-263 (1302.), class-261 (981.), class-267 (761.), class-260 (646.), class-264 (446.), class-265 (211.), class-266 (75.), class-268 (60.), class-259 (58.), class-269 (0.).

* The cosine of an angle (cos) 772. between the radius of the center of the class -263 and axis, class-261 (761.), class-262 (-740.), class-264 (504.), class-260 (-497.), class-267 (389.), class-265 (-236.), class-259 (-207.), class-266 (158.), class-268 (91.), class-269 (0.).

Table 118 Center of hierarchical classification classes in relation to the factors axis 2 (factor variance: 1.9782)

knot

knot1

knot2

weight

inr

dst

(F2)2

acor

cor

ctr

cos

+cos2

269

265

268

1000

894

10731

268

262

267

778

612

9445

567

321

250

126

185

267

266

263

622

419

8085

434

188

117

153

174

266

264

259

422

251

7139

887

787

332

110

168

332

135

265

260

257

222

315

17032

-1984

3935

874

231

442

-481

287

264

258

252

193

146

9100

1397

1951

376

214

190

463

469

263

232

261

200

182

10926

-523

273

-158

621

262

253

244

156

218

16800

1098

1206

188

268

619

261

251

250

163

141

10400

-239

-74

585

260

248

256

104

218

25172

-1784

3182

330

126

167

-356

374

259

249

255

230

112

5870

459

211

190

* Absolute contribution (acor) 874. class-265 followed by absolute contribution for: class-264 (376.), class-266 (332.), class-260 (330.), class-268 (250.), class-262 (188.), class-267 (117.), class-263 (55.), class-259 (48.), class-261 (9.), class-269 (0.).

* The cosine of an angle (cos) -481. between the radius of the center of the class -265 and axis, class-264 (463.), class-260 (-356.), class-266 (332.), class-262 (268.), class-259 (190.), class-268 (185.), class-263 (-158.), class-267 (153.), class-261 (-74.), class-269 (0.).

Table 119 Center of hierarchical classification classes in relation to the factors axis 3 (factor variance: 1.5492)

knot

knot1

knot2

weight

inr

dst

(F3)2

acor

cor

ctr

cos

+cos2

269

265

268

1000

894

10731

268

262

267

778

612

9445

-33

-11

267

266

263

622

419

8085

175

266

264

259

422

251

7139

183

140

265

260

257

222

315

17032

115

287

264

258

252

193

146

9100

353

124

117

482

263

232

261

200

182

10926

-318

101

-96

630

262

253

244

156

218

16800

-251

-61

622

261

251

250

163

141

10400

-409

168

-127

601

260

248

256

104

218

25172

215

376

259

249

255

230

112

5870

* Absolute contribution (acor) 27. class-261 followed by absolute contribution for: class-264 (24.), class-263 (20.), class-266 (14.), class-262 (10.), class-260 (5.), class-265 (3.), class-268 (1.), class-269 (0.), class-267 (0.), class-259 (0.).

* The cosine of an angle (cos) -127. between the radius of the center of the class -261 and axis, class-264 (117.), class-263 (-96.), class-266 (68.), class-262 (-61.), class-260 (43.), class-265 (28.), class-259 (17.), class-268 (-11.), class-267 (8.), class-269 (0.).

Analysis of differences between two nodes (dipoles) of hierarchical classification classes

Table 120 Dipoles of the 11 highest nodes in relation to the factors axes from 1 to 3

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qld

cod

ctd

cod

ctd

cod

ctd

269

265

268

1000

3502

-1252

678

-2551

2814

568

148

268

262

267

778

7359

-4137

7143

446

664

184

-272

267

266

263

622

5463

-2131

3659

129

1410

1601

136

501

202

266

264

259

422

6158

2023

4971

938

1068

313

119

265

260

257

222

7444

-2853

7287

375

126

188

264

258

252

193

7339

1867

5592

-713

815

-762

931

263

232

261

200

3601

527

349

-1531

2948

492

304

262

253

244

156

3735

-712

880

-1254

2732

-267

123

261

251

250

163

7521

1962

7469

163

-4

260

248

256

104

5376

-594

477

-1463

2896

1217

2003

259

249

255

230

5344

-1038

3751

-670

1564

As shown in Table 120 we found that Inertia of the dipole (ind) a(n) b(n) is 33, that is, the inertia of the whole system, class-269 , followed by dipoles: class-268 (25.), class-267 (14.), class-266 (7.), class-265 (5.), class-264 (2.), class-263 (2.), class-262 (2.), class-261 (2.), class-260 (1.), class-259 (1.).

* The quality of the observed factors (qld) 7521. is high, for class-261 (dipole) which represents the quality of the vector ab representation in the factors space of this research, the other qualities are for: class-265 (7444.-high), class-268 (7359.-high), class-264 (7339.-high), class-266 (6158.-high), class-267 (5463.-high), class-260 (5376.-high), class-259 (5344.-high), class-262 (3735.-high), class-263 (3601.-high), class-269 (3502.-high).

* Projection ab on the axis 1st-isolated factor, that is, the projection of the dipole class-268 is -4137, other dipole projections on the axis are: class-265 (-2853.), class-267 (-2131.), class-266 (2023.), class-261 (1962.), class-264 (1867.), class-269 (-1252.), class-259 (-1038.), class-262 (-712.), class-260 (-594.), class-263 (527.). Projection ab on the axis 2nd-isolated factor, that is, the projection of the dipole class-269 is -2551, other dipole projections on the axis are: class-263 (-1531.), class-260 (-1463.), class-267 (1410.), class-262 (-1254.), class-266 (938.), class-264 (-713.), class-259 (-670.), class-268 (664.), class-265 (375.), class-261 (163.). Projection ab on the axis 3rd-isolated factor, that is, the projection of the dipole class-260 is 1217, other dipole projections on the axis are: class-264 (-762.), class-267 (501.), class-263 (492.), class-266 (313.), class-268 (-272.), class-262 (-267.), class-265 (188.), class-269 (148.), class-259 (91.), class-261 (-4.).

* Relative contribution of the 1st-factor axis (D1), dipole a(n) b(n) is class-261 is 7469. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-265 (7287.-high), class-268 (7143.-high), class-264 (5592.-high), class-266 (4971.-high), class-259 (3751.-high), class-267 (3659.-high), class-262 (880.-high), class-269 (678.-high), class-260 (477.-intermediate), class-263 (349.-low). Relative contribution of the 2nd-factor axis (D2), dipole a(n) b(n) is class-263 is 2948. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-260 (2896.-high), class-269 (2814.-high), class-262 (2732.-high), class-267 (1601.-high), class-259 (1564.-high), class-266 (1068.-high), class-264 (815.-high), class-268 (184.-without significance), class-265 (126.-without significance), class-261 (52.-without significance). Relative contribution of the 3rd-factor axis (D3), dipole a(n) b(n) is class-260 is 2003. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-264 (931.-high), class-263 (304.-low), class-267 (202.-without significance), class-262 (123.-without significance), class-266 (119.-without significance), class-265 (32.-without significance), class-268 (31.-without significance), class-259 (29.-without significance), class-269 (9.-without significance), class-261 (0.-without significance).

* Relative contribution of dipoles (ctd) class-268 to axis of the 1st-factor is 7143, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-267 (3659.), class-265 (7287.), class-266 (4971.), class-269 (678.), class-261 (7469.), class-264 (5592.), class-259 (3751.), class-262 (880.), class-263 (349.), class-260 (477.). Relative contribution of dipoles (ctd) class-269 to axis of the 2nd-factor is 2814, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-267 (1601.), class-266 (1068.), class-263 (2948.), class-262 (2732.), class-268 (184.), class-260 (2896.), class-259 (1564.), class-264 (815.), class-265 (126.), class-261 (52.). Relative contribution of dipoles (ctd) class-260 to axis of the 3rd-factor is 2003, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-267 (202.), class-264 (931.), class-266 (119.), class-268 (31.), class-263 (304.), class-269 (9.), class-262 (123.), class-265 (32.), class-261 (0.), class-259 (29.).

Table 121 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 1

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

269

265

268

173

400

-1252

1567

271

678

-823

678

268

262

267

124

383

-4137

17113

2130

7143

446

-2673

7143

267

266

263

136

271

-2131

4541

616

3659

129

-1913

3659

266

264

259

105

204

2023

4093

429

4971

2230

4971

265

260

257

278

-2853

8139

450

7287

-2699

7287

264

258

252

133

1867

3486

143

5592

2365

5592

263

232

261

120

527

278

349

591

349

262

253

244

144

-712

506

880

-938

880

261

251

250

128

1962

3850

156

7469

2733

7469

260

248

256

170

-594

353

477

-691

477

259

249

255

-1038

1077

3751

-1937

3751

As shown in Table 121 the greatest distance (dst) 400. between the center of the cloud and the center of the class-269, it is followed by: class-268 (383.), class-265 (278.), class-267 (271.), class-266 (204.), class-260 (170.), class-262 (144.), class-264 (133.), class-261 (128.), class-263 (120.), class-259 (68.).

* Absolute contribution (acor) 2130. class-268 followed by absolute contribution for: class-267 (616.), class-265 (450.), class-266 (429.), class-269 (271.), class-261 (156.), class-264 (143.), class-259 (59.), class-262 (20.), class-263 (8.), class-260 (8.).

* The cosine of an angle (cos) 2733. between the radius of the center of the class -261 and axis, class-265 (-2699.), class-268 (-2673.), class-264 (2365.), class-266 (2230.), class-259 (-1937.), class-267 (-1913.), class-262 (-938.), class-269 (-823.), class-260 (-691.), class-263 (591.).

Table 122 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 2

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

269

265

268

173

400

-2551

6505

1124

2814

568

-1678

3492

268

262

267

124

383

664

441

184

429

7328

267

266

263

136

271

1410

1987

270

1601

136

1265

5261

266

264

259

105

204

938

879

106

1033

6039

265

260

257

278

375

141

126

355

7413

264

258

252

133

-713

508

815

-903

6408

263

232

261

120

-1531

2345

2948

-1717

3297

262

253

244

144

-1254

1573

2732

-1653

3612

261

251

250

128

163

227

7521

260

248

256

170

-1463

2142

2896

-1702

3373

259

249

255

-670

449

1564

-1251

5315

* Absolute contribution (acor) 2130. of the class class-268, followed by absolute contribution for: class-267 (616.), class-265 (450.), class-266 (429.), class-269 (271.), class-261 (156.), class-264 (143.), class-259 (59.), class-262 (20.), class-263 (8.), class-260 (8.).

Table 123 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 3

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

269

265

268

173

400

148

3502

268

262

267

124

383

-272

-176

7359

267

266

263

136

271

501

251

202

450

5463

266

264

259

105

204

313

119

344

6158

265

260

257

278

188

177

7444

264

258

252

133

-762

580

931

-965

7339

263

232

261

120

492

242

304

551

3601

262

253

244

144

-267

123

-351

3735

261

251

250

128

-4

-6

7521

260

248

256

170

1217

1481

2003

1415

5376

259

249

255

170

5344

* Absolute contribution (acor) 2130. of the class-268 followed by absolute contribution for: class-267 (616.), class-265 (450.), class-266 (429.), class-269 (271.), class-261 (156.), class-264 (143.), class-259 (59.), class-262 (20.), class-263 (8.), class-260 (8.).

Table 124 Relative mutual contributions of factors (from 1 to 3) per classes

kls

knot1

knot2

Q(n)

inr

+inr

269

265

268

173

268

262

267

124

177

267

266

263

136

266

264

259

105

265

260

257

264

258

252

263

232

261

262

253

244

261

251

250

260

248

256

259

249

255

Significance of dipole association coefficient (class) Q(n) is the highest for the class-269 (173.) followed by: class-267 (136.), class-268 (124.), class-266 (105.), class-265 (55.), class-259 (54.), class-264 (41.), class-261 (40.), class-262 (39.), class-263 (30.), class-260 (24.).

* Inertia is 33 for the class-269 this means that it stands out most prominently, it is followed by: class-268 (25.), class-267 (14.), class-266 (7.), class-265 (5.), class-264 (2.), class-263 (2.), class-262 (2.), class-261 (2.), class-260 (1.), class-259 (1.).

* The contribution of the 1st- isolated factor to the class-268 is 177, this means that examinees who belong to the class-268 have anthropometric and linear hepatic characteristics of the 1st-factors structure, followed by: class-267 (51.), class-265 (38.), class-266 (36.), class-269 (23.), class-261 (13.), class-264 (12.), class-259 (5.), class-262 (2.), class-263 (1.), class-260 (1.). The contribution of the 2nd- isolated factor to the class-269 is 94. followed by: class-267 (22.), class-266 (8.), class-263 (6.), class-268 (5.), class-262 (5.), class-260 (4.), class-264 (2.), class-259 (2.), class-265 (1.), class-261 (0.). The contribution of the 3rd- isolated factor to the class-267 is 3. followed by: class-260 (3.), class-264 (2.), class-268 (1.), class-266 (1.), class-263 (1.), class-269 (0.), class-265 (0.), class-262 (0.), class-261 (0.), class-259 (0.).

*The highest contribution of the factor to the class-269 (94.) has the 1st- factor, this means that mentioned structure have examinees of the observed class. The same can be said, with less contribution, for characteristics: factor-2 (23.), factor-3 (0.). The contribution to the class-268 (177.) belongs to 1.- factor and factor-2 (5.), factor-3 (1.). The contribution to the class-267 (51.) belongs to 1.- factor and factor-2 (22.), factor-3 (3.). The contribution to the class-266 (36.) belongs to 1.- factor and factor-2 (8.), factor-3 (1.). The contribution to the class-265 (38.) belongs to 1.- factor and factor-2 (1.), factor-3 (0.). The contribution to the class-264 (12.) belongs to 1.- factor and factor-2 (2.), factor-3 (2.). The contribution to the class-263 (6.) belongs to 1.- factor and factor-2 (1.), factor-3 (1.). The contribution to the class-262 (5.) belongs to 1.- factor and factor-2 (2.), factor-3 (0.). The contribution to the class-261 (13.) belongs to 1.- factor and factor-2 (0.), factor-3 (0.). The contribution to the class-260 (4.) belongs to 1.- factor and factor-2 (3.), factor-3 (1.). The contribution to the class-259 (5.) belongs to 1.- factor and factor-2 (2.), factor-3 (0.).

Presentation of isolated classes

Significance of dipole association coefficient (class) Q(n) is the highest for the class-267 (136.) followed by: class-265 (55.) and class-262 (39.).

* Inertia is 14. For the class-267, this means that it stands out most prominently, it is followed by: class-265 (5.), class-262 (2.).

* The contribution of the 1st- isolated factor to the class-267 is 51. followed by: class-265 (38.), class-262 (2.). The contribution of the 2nd- isolated factor to the class-267 is 22. followed by: class-262 (5.), class-265 (1.). The contribution of the 3rd- isolated factor to the class-267 is 3. followed by: class-265 (0.), class-262 (0.).

*, factor-3 (0.), factor-3 (1.), factor-3 (3.), factor-3 (1.), factor-3 (0.), factor-3 (2.), factor-3 (1.), factor-3 (0.), factor-3 (0.), factor-2 (3.), factor-3 (0.).

Analysis of the structure for anthropometric and linear hepatic measurements

In accordance to the previously established design of the study, it was planned to extract optimal number of factors, using factor analysis of principal components from the sample of 103 examinees, on the basis of 12 anthropometric and linear hepatic measurements: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal). The aim is to find the associations between individual variables, to determine the contribution of each factor to a variable, contribution of each variable to a factor, to apply complementary analyses and to present the results Graphically. The coordinates of the variables for anthropometric and linear hepatic measurements will be presented to determine their position in an isolated structure.

Structure 3 isolated factors for anthropometric and linear hepatic measurements

Table 125 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

407

1000

BMI

-243

784

1000

D-il

102

461

411

1000

ApBo

163

564

494

471

1000

TvBo

194

628

548

342

597

1000

MxAp

205

515

403

384

472

396

1000

MxCo

107

158

-16

1000

MxCr

140

274

191

307

244

203

101

251

1000

MxCc

159

392

302

391

318

289

226

916

1000

Comx

151

226

155

122

335

301

192

719

267

324

1000

Vcal

204

443

334

369

387

380

507

665

726

731

610

1000

We found the strongest correlations (916) between Max CC (MxCc) and Maximal Crainocaudal (MxCr) . The strongest negative correlation is -243 between BMI (BMI) and height (hgt).

Table 126 The characteristic square of a factor and the percentage contribution

sqare

sum

4.867

40.556

2.046

17.051

57.607

1.316

10.964

68.571

1.174

9.782

78.353

.724

6.030

84.383

.625

5.212

89.596

.548

4.570

94.165

.373

3.107

97.272

.248

2.068

99.340

.070

.581

99.921

.007

.057

99.978

.003

.022

100.000

Percentage representation of the characteristic squares fall in the range between .022% do 40.556%. The new structure is consisted of 3 isolated factors which contain 68.571 % information from the whole sample.

Table 127 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

142

283

-80

236

wgt

788

779

606

125

416

173

BMI

648

638

407

489

239

117

-41

D-il

486

597

356

272

-237

ApBo

621

696

484

100

344

118

134

TvBo

631

683

466

325

106

243

MxAp

495

595

354

348

121

142

MxCo

842

404

163

-682

465

227

462

214

163

MxCr

943

634

402

-444

197

-586

343

261

MxCc

930

724

524

108

-338

114

-540

292

222

Comx

798

557

310

-491

241

118

497

247

188

Vcal

905

845

713

147

-437

191

-18

12.0

1000

The isolated factors structures for anthropometric and linear hepatic measurements

Whole sample that consisted of 12 anthropometric and linear hepatic measurements was reduced to 3 isolated factors. Contribution of isolated factor (qlt) is significant for 11 anthropometric and linear hepatic measurements.

* The communality is higher for: Maximal Crainocaudal (MxCr) 943, Max CC (MxCc) 930, liver volume (calculated by formula) (Vcal) 905, Maximal Coronal (MxCo) 842, Cormax LL (Comx) 798, weight (wgt) 788, BMI (BMI) 648, Transverse body dimension (TvBo) 631, AP body dimension (ApBo) 621.

* Decreased communality shows that the structure of 3 isolated factors does not contain enough information about 1 anthropometric and linear hepatic measurement: height (hgt) 142

The variables that contribute in forming the structure of each isolated factor are: Maximal Crainocaudal, Max CC, liver volume (calculated by formula), Maximal Coronal, Cormax LL, weight, BMI, Transverse body dimension, AP body dimension, Maximal Ap, Diaphragm to iliac, the variable that does not not contribute to factor structure is: height.

* Structure of the 1st- isolated factor is formed of 7 anthropometric and linear hepatic measurements: liver volume (calculated by formula) (Vcal) with factor contribution (cor) 714, weight (wgt) 607, Max CC (MxCc) 525, AP body dimension (ApBo) 485, Transverse body dimension (TvBo) 467, BMI (BMI) 407, Maximal Crainocaudal (MxCr) 403. Latent variables are: Diaphragm to iliac (D-il) 357, Maximal Ap (MxAp) 354, Cormax LL (Comx) 310. Association liver volume (calculated by formula) is in concordance with: weight, Max CC, AP body dimension, Transverse body dimension, BMI, Maximal Crainocaudal, Diaphragm to iliac, Maximal Ap, Cormax LL.

* Structure of the 2nd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: Maximal Coronal (MxCo) with factor contribution (cor) 465.

* Structure of the 3rd- isolated factor is formed of 2 latent anthropometric and linear hepatic measurements: Maximal Crainocaudal (MxCr) with factor contribution (cor) 344, Max CC (MxCc) 292. Association Maximal Crainocaudal is in concordance with: Max CC.

* Several factors contribute to variable for: Maximal Crainocaudal, factor-1 (403), factor-3 (344), Max CC, factor-1 (525), factor-3 (292).

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

The analysis of the sample consisting of 103 examinees revealed that in forming the structure of 3 isolated factors 58 (56.31%) have high contribution, intermediate contribution have 23 (22.33%) examinees, with low contribution , without significance are 22 (21.36%) examinees.

1. – for 36 (34.95%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 17 (16.50%) examinees. For 23 we found direct proportionality, and 30 examinees are inversely related.

2. – for 15 (14.56%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure13 (12.62%). For 14 we found direct proportionality, and for 14 are inversely related.

3. – for 6 (5.83%) anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure are 5 (4.85%) examinees. For 7 examinees we found direct proportionality, and 4 examinees are inversely related.

Concordance of anthropometric and linear hepatic measurements with the structure: one factor have 57 examinees, latent agreement only have 24 examinees, with no agreement are 22 examinees.

It should be noted that 5 examinees stands out from the rest (inr)

Graph 41 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 42 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 43 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 44 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Clustering on isolated factors for anthropometric and linear hepatic measurements

In this part of the study we clusterised 103 examinees based on 3 isolated factors from 12 anthropometric and linear hepatic measurements

Sum of the levels of measures1.379

Table 129 Levels of grouping on the isolated factors

class

distance

class1

class2

nbr.elemn.

205

471

204

202

103

204

273

201

203

148

196

198

202

107

188

200

201

199

193

200

195

197

199

194

181

198

191

189

197

192

162

196

186

187

195

177

182

194

165

190

Group-1 (knot 201) contain 33 , is consisted of sublevels, knots 199 and 193, the distance between them is 79. Group-2 (knot 202) contain 31 , is consisted of sublevels, knots 188 and 200, the distance between them is 107. Group-3 (knot 203) contain 39, is consisted of sublevels, knots 196 and 198 and the distance between them is 149.

Mutual contributions of hierarchical classification classes and isolated factor structures anthropometric and linear hepatic measurements

In this part of the study we analysed 11 higher classes of hierarchical classification and 3 isolated classes from the sample consisting of 103 examinees in relation to 3 isolated factors structure for the anthropometric and linear hepatic measurements. Isolated classes are: 201, 202, 203.

Centers of hierarchical classification classes and isolated factors

Table 130 Centers of 3 hierarchical classification classes in relation to 3 isolated factors structures

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qlt

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

205

204

202

1000

885

204

201

203

699

637

399

695

165

203

196

198

379

354

218

-838

1306

152

316

181

202

188

200

301

288

304

-927

-1614

227

383

-132

201

199

193

320

306

303

1862

303

228

-27

-89

200

195

197

262

226

405

-1472

210

117

-1408

192

254

-196

199

194

181

155

229

588

3210

582

329

-336

-35

198

191

189

233

202

483

-2053

405

202

900

197

192

162

126

107

482

-889

-2026

404

253

-86

196

186

187

146

164

385

1105

1957

283

273

387

195

177

182

136

122

447

-2013

375

113

-834

-298

As shown in Table 130 we found that the highest weight was 379. for isolated class-203 This means that the biggest part of the sample which belongs to one class, belongs to this class which corresponds to the specified weighting factor, it is followed by: class-201 (320.), class-202 (301.).

* Inertia 885. class-205 this means that it stands out most prominently, it is followed by: class-204 (637.), class-203 (354.), class-201 (306.), class-202 (288.), class-199 (229.), class-200 (226.), class-198 (202.), class-196 (164.), class-195 (122.), class-197 (107.).

* Contribution of isolated factors 588. is intermediate, for class-199 this means that isolated factors gives the most information to this class, then for: class-198 (483.-intermediate), class-197 (482.-intermediate), class-195 (447.-intermediate), class-200 (405.-intermediate), class-196 (385.-low), class-202 (304.-low), class-201 (303.-low), class-203 (218.-without significance), class-204 (59.-without significance), class-205 (0.-without significance).

* Relative contribution of the 1st-isolated factor to the center of the class-199 is 582. intermediate, this means that factor gives the most information to this class, then for: center of the class-198 (405.-intermediate), center of the class-195 (375.-low), center of the class-201 (303.-low), center of the class-200 (210.-without significance), center of the class-196 (90.-without significance), center of the class-197 (78.-without significance), center of the class-202 (75.-without significance), center of the class-203 (63.-without significance), center of the class-204 (15.-without significance), center of the class-205 (0.-without significance). Relative contribution of the 2nd-isolated factor to the center of the class-197 is 404. intermediate, then for: center of the class-196 (283.-low), center of the class-202 (227.-without significance), center of the class-200 (192.-without significance), center of the class-203 (152.-without significance), center of the class-198 (78.-without significance), center of the class-195 (64.-without significance), center of the class-204 (44.-without significance), center of the class-199 (6.-without significance), center of the class-205 (0.-without significance), center of the class-201 (0.-without significance). Relative contribution of the 3rd-isolated factor to the center of the class-196 is 11. without significance, then for: center of the class-195 (8.-without significance), center of the class-200 (4.-without significance), center of the class-203 (3.-without significance), center of the class-202 (2.-without significance), center of the class-201 (1.-without significance), center of the class-197 (1.-without significance), center of the class-205 (0.-without significance), center of the class-204 (0.-without significance), center of the class-199 (0.-without significance), center of the class-198 (0.-without significance).

* Association of the cluster for the 1st- factors structure is proportional between classes-205, class-201, class-197, class-199, inversely proportional with, class-203, class-202, class-200, class-198, class-197, class-195.

* Association of the cluster for the 2nd- factors structure is proportional between classes-205, class-203, class-205, class-199, inversely proportional with, class-202, class-201, class-200, class-199, class-197, class-195.

* Association of the cluster for the 3rd- factors structure is proportional between classes-205, class-203, class-205, class-199, inversely proportional with, class-202, class-201, class-200, class-199, class-197, class-195.

Table 131 Center of hierarchical classification classes in relation to the factors axis 1 (factor variance: 4.8667)

knot

knot1

knot2

weight

inr

dst

(F1)2

acor

cor

ctr

cos

+cos2

205

204

202

1000

885

10621

204

201

203

699

637

10933

399

159

111

121

203

196

198

379

354

11210

-838

703

266

-250

202

188

200

301

288

11464

-927

860

259

-274

201

199

193

320

306

11460

1862

3467

1111

303

228

550

303

200

195

197

262

226

10325

-1472

2165

568

210

117

-458

210

199

194

181

155

229

17712

3210

10305

1601

582

329

763

582

198

191

189

233

202

10410

-2053

4214

982

405

202

-636

405

197

192

162

126

107

10168

-889

790

100

-279

196

186

187

146

164

13510

1105

1221

178

301

195

177

182

136

122

10805

-2013

4050

551

375

113

-612

375

As shown in Table() the greatest distance (dst) 17712. between the center of the cloud and the center of the class-199 , it is followed by: class-196 (13510.), class-202 (11464.), class-201 (11460.), class-203 (11210.), class-204 (10933.), class-195 (10805.), class-205 (10621.), class-198 (10410.), class-200 (10325.), class-197 (10168.).

* Absolute contribution (acor) 1601. class-199 followed by absolute contribution for: class-201 (1111.), class-198 (982.), class-200 (568.), class-195 (551.), class-203 (266.), class-202 (259.), class-196 (178.), class-204 (111.), class-197 (100.), class-205 (0.).

* The cosine of an angle (cos) 763. between the radius of the center of the class -199 and axis, class-198 (-636.), class-195 (-612.), class-201 (550.), class-200 (-458.), class-196 (301.), class-197 (-279.), class-202 (-274.), class-203 (-250.), class-204 (121.), class-205 (0.).

Table 132 Center of hierarchical classification classes in relation to the factors axis 2 (factor variance: 2.0461)

knot

knot1

knot2

weight

inr

dst

(F2)2

acor

cor

ctr

cos

+cos2

205

204

202

1000

885

10621

204

201

203

699

637

10933

695

483

338

165

210

203

196

198

379

354

11210

1306

1707

646

152

316

390

215

202

188

200

301

288

11464

-1614

2606

784

227

383

-477

302

201

199

193

320

306

11460

-27

-8

303

200

195

197

262

226

10325

-1408

1982

520

192

254

-438

402

199

194

181

155

229

17712

-336

113

-80

588

198

191

189

233

202

10410

900

810

189

279

483

197

192

162

126

107

10168

-2026

4105

518

404

253

-635

481

196

186

187

146

164

13510

1957

3830

558

283

273

533

374

195

177

182

136

122

10805

-834

695

-254

439

* Absolute contribution (acor) is 784. for the class-202 followed by absolute contribution for: class-203 (646.), class-196 (558.), class-200 (520.), class-197 (518.), class-204 (338.), class-198 (189.), class-195 (95.), class-199 (18.), class-205 (0.), class-201 (0.).

* The cosine of an angle (cos) -635. between the radius of the center of the class -197 and axis, class-196 (533.), class-202 (-477.), class-200 (-438.), class-203 (390.), class-198 (279.), class-195 (-254.), class-204 (210.), class-199 (-80.), class-201 (-8.), class-205 (0.).

Table 133 Center of hierarchical classification classes in relation to the factors axis 3 (factor variance: 1.3156)

knot

knot1

knot2

weight

inr

dst

(F3)2

acor

cor

ctr

cos

+cos2

205

204

202

1000

885

10621

204

201

203

699

637

10933

203

196

198

379

354

11210

181

218

202

188

200

301

288

11464

-132

-39

304

201

199

193

320

306

11460

-89

-27

303

200

195

197

262

226

10325

-196

-61

405

199

194

181

155

229

17712

-35

-8

588

198

191

189

233

202

10410

483

197

192

162

126

107

10168

-86

-27

482

196

186

187

146

164

13510

387

150

105

385

195

177

182

136

122

10805

-298

-91

447

* Absolute contribution (acor) 22. class-196 followed by absolute contribution for: class-203 (12.), class-195 (12.), class-200 (10.), class-202 (5.), class-201 (3.), class-204 (2.), class-198 (1.), class-197 (1.), class-205 (0.), class-199 (0.).

* The cosine of an angle (cos) 105. between the radius of the center of the class -196 and axis, class-195 (-91.), class-200 (-61.), class-203 (54.), class-202 (-39.), class-201 (-27.), class-197 (-27.), class-204 (17.), class-198 (16.), class-199 (-8.), class-205 (0.).

Analysis of differences between two nodes (dipoles) of hierarchical classification classes

Table 134 Dipoles of the 11 highest nodes in relation to the factors axes from 1 to 3

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qld

cod

ctd

cod

ctd

cod

ctd

205

204

202

1000

3181

1327

785

2310

2380

548

189

204

201

203

699

5795

2700

4621

260

-1334

1128

151

-270

203

196

198

379

6754

3158

6012

184

1057

674

336

202

188

200

301

6486

4216

5602

124

-1601

807

493

201

199

193

320

7334

2617

6957

113

-599

365

106

200

195

197

262

3924

-1124

1816

1192

2044

-212

199

194

181

155

9160

-2404

5439

-956

861

1743

2860

198

191

189

233

7853

2022

7726

-246

114

197

192

162

126

6305

2037

5063

898

983

-460

259

196

186

187

146

7758

2103

6974

-478

360

519

425

195

177

182

136

7486

-1766

5847

-623

727

697

911

As shown in Table 134 we found that Inertia of the dipole (ind) a(n) b(n) is 39, that is, the inertia of the whole system, class-205 , followed by dipoles: class-204 (23.), class-203 (12.), class-202 (9.), class-201 (7.), class-200 (4.), class-199 (3.), class-198 (2.), class-197 (2.), class-196 (2.), class-195 (1.).

* The quality of the observed factors (qld) 9160. is high, for the class-199 (dipole) which represents the quality of the vector ab representation in the factors space of this research, other qualities are for: class-198 (7853.-high), class-196 (7758.-high), class-195 (7486.-high), class-201 (7334.-high), class-203 (6754.-high), class-202 (6486.-high), class-197 (6305.-high), class-204 (5795.-high), class-200 (3924.-high), class-205 (3181.-high).

* Projection ab on the axis 1st-isolated factor, that is, the projection of the dipole class-202 is 4216, other dipole projections on the axis are: class-203 (3158.), class-204 (2700.), class-201 (2617.), class-199 (-2404.), class-196 (2103.), class-197 (2037.), class-198 (2022.), class-195 (-1766.), class-205 (1327.), class-200 (-1124.). Projection ab on the axis 2nd-isolated factor, that is, the projection of the dipole class-205 is 2310, other dipole projections on the axis are: class-202 (-1601.), class-204 (-1334.), class-200 (1192.), class-203 (1057.), class-199 (-956.), class-197 (898.), class-195 (-623.), class-201 (-599.), class-196 (-478.), class-198 (-246.). Projection ab on the axis 3rd-isolated factor, that is, the projection of the dipole class-199 is 1743, other dipole projections on the axis are: class-195 (697.), class-196 (519.), class-202 (493.), class-197 (-460.), class-203 (336.), class-204 (-270.), class-200 (-212.), class-205 (189.), class-201 (106.), class-198 (81.).

* Relative contribution of the 1st-factor axis (D1), dipole a(n) b(n) is class-198 is 7726. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-196 (6974.-high), class-201 (6957.-high), class-203 (6012.-high), class-195 (5847.-high), class-202 (5602.-high), class-199 (5439.-high), class-197 (5063.-high), class-204 (4621.-high), class-200 (1816.-high), class-205 (785.-high). Relative contribution of the 2nd-factor axis (D2), dipole a(n) b(n) is class-205 is 2380. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-200 (2044.-high), class-204 (1128.-high), class-197 (983.-high), class-199 (861.-high), class-202 (807.-high), class-195 (727.-high), class-203 (674.-high), class-201 (365.-low), class-196 (360.-low), class-198 (114.-without significance). Relative contribution of the 3rd-factor axis (D3), dipole a(n) b(n) is class-199 is 2860. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-195 (911.-high), class-196 (425.-intermediate), class-197 (259.-without significance), class-202 (77.-without significance), class-203 (68.-without significance), class-200 (65.-without significance), class-204 (46.-without significance), class-205 (16.-without significance), class-198 (12.-without significance), class-201 (11.-without significance).

* Relative contribution of dipoles (ctd) class-204 to axis of the 1st-factor is 4621, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-203 (6012.), class-202 (5602.), class-201 (6957.), class-205 (785.), class-198 (7726.), class-199 (5439.), class-196 (6974.), class-197 (5063.), class-195 (5847.), class-200 (1816.). Relative contribution of dipoles (ctd) class-205 to axis of the 2nd-factor is 2380, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-204 (1128.), class-203 (674.), class-200 (2044.), class-202 (807.), class-201 (365.), class-199 (861.), class-197 (983.), class-195 (727.), class-196 (360.), class-198 (114.). Relative contribution of dipoles (ctd) class-199 to axis of the 3rd-factor is 2860, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-195 (911.), class-204 (46.), class-203 (68.), class-196 (425.), class-205 (16.), class-202 (77.), class-197 (259.), class-200 (65.), class-201 (11.), class-198 (12.).

Table 135 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 1

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

205

204

202

210

472

1327

1760

370

785

886

785

204

201

203

174

392

2700

7291

1265

4621

260

2150

4621

203

196

198

393

3158

9972

894

6012

184

2452

6012

202

188

200

357

4216

17778

601

5602

124

2367

5602

201

199

193

246

2617

6849

548

6957

113

2638

6957

200

195

197

174

-1124

1263

1816

-1348

1816

199

194

181

199

-2404

5779

168

5439

-2332

5439

198

191

189

118

2022

4090

212

7726

2780

7726

197

192

162

194

2037

4150

124

5063

2250

5063

196

186

187

158

2103

4424

160

6974

2641

6974

195

177

182

122

-1766

3119

5847

-2418

5847

As shown in Table 135 the greatest distance (dst) 472. between the center of the cloud and the center of the class-205, it is followed by: class-203 (393.), class-204 (392.), class-202 (357.), class-201 (246.), class-199 (199.), class-197 (194.), class-200 (174.), class-196 (158.), class-195 (122.), class-198 (118.).

* Absolute contribution (acor) is 1265. for the class-204 followed by absolute contribution for: class-203 (894.), class-202 (601.), class-201 (548.), class-205 (370.), class-198 (212.), class-199 (168.), class-196 (160.), class-197 (124.), class-195 (97.), class-200 (83.).

* The cosine of an angle (cos) 2780. between the radius of the center of the class -198 and axis, class-196 (2641.), class-201 (2638.), class-203 (2452.), class-195 (-2418.), class-202 (2367.), class-199 (-2332.), class-197 (2250.), class-204 (2150.), class-200 (-1348.), class-205 (886.).

Table 136 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 2

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

205

204

202

210

472

2310

5334

1122

2380

548

1543

3165

204

201

203

174

392

-1334

1779

309

1128

151

-1062

5749

203

196

198

393

1057

1117

100

674

821

6686

202

188

200

357

-1601

2562

807

-899

6410

201

199

193

246

-599

359

365

-604

7322

200

195

197

174

1192

1421

2044

1430

3859

199

194

181

199

-956

915

861

-928

6300

198

191

189

118

-246

114

-338

7840

197

192

162

194

898

806

983

992

6046

196

186

187

158

-478

228

360

-600

7334

195

177

182

122

-623

388

727

-853

6575

* Absolute contribution (acor) 1265. class-204 followed by absolute contribution for: class-203 (894.), class-202 (601.), class-201 (548.), class-205 (370.), class-198 (212.), class-199 (168.), class-196 (160.), class-197 (124.), class-195 (97.), class-200 (83.).

Table 137 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 3

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

205

204

202

210

472

189

126

3181

204

201

203

174

392

-270

-215

5795

203

196

198

393

336

113

261

6754

202

188

200

357

493

243

277

6486

201

199

193

246

106

107

7334

200

195

197

174

-212

-254

3924

199

194

181

199

1743

3039

2860

1691

9160

198

191

189

118

112

7853

197

192

162

194

-460

212

259

-509

6305

196

186

187

158

519

270

425

652

7758

195

177

182

122

697

486

911

954

7486

Table 138 Relative mutual contributions of factors (from 1 to 3) per classes

kls

knot1

knot2

Q(n)

inr

+inr

205

204

202

210

204

201

203

174

105

203

196

198

202

188

200

201

199

193

200

195

197

199

194

181

198

191

189

197

192

162

101

196

186

187

103

195

177

182

104

Significance of dipole association coefficient (class) Q(n) is the highest for the class-205 (210.) followed by: class-204 (174.), class-203 (90.), class-201 (80.), class-200 (65.), class-198 (52.), class-196 (36.), class-202 (34.), class-195 (31.), class-197 (30.), class-199 (29.).

* Inertia is 39. for the class-205 this means that it stands out most prominently, it is followed by: class-204 (23.), class-203 (12.), class-202 (9.), class-201 (7.), class-200 (4.), class-199 (3.), class-198 (2.), class-197 (2.), class-196 (2.), class-195 (1.).

* The contribution of the 1st- isolated factor to the class-204 is 105, this means that examinees who belong to the class-204 have anthropometric and linear hepatic characteristics of the 1st-factors structure, followed by: class-203 (74.), class-202 (50.), class-201 (46.), class-205 (31.), class-198 (18.), class-199 (14.), class-196 (13.), class-197 (10.), class-195 (8.), class-200 (7.). The contribution of the 2nd- isolated factor to the class-205 is 94. followed by: class-204 (26.), class-203 (8.), class-200 (8.), class-202 (7.), class-201 (2.), class-199 (2.), class-197 (2.), class-196 (1.), class-195 (1.), class-198 (0.). The contribution of the 3rd- isolated factor to the class-199 is 7. followed by: class-205 (1.), class-204 (1.), class-203 (1.), class-202 (1.), class-197 (1.), class-196 (1.), class-195 (1.), class-201 (0.), class-200 (0.), class-198 (0.).

*The highest contribution of the factor to the class-205 (94.) has the 1st- factor, this means that mentioned structure have examinees of the observed class. The same can be said, with less contribution, for the characteristics: factor-2 (31.), factor-3 (1.). The contribution to the class-204 (105.) belongs to 1.- factor and factor-2 (26.), factor-3 (1.). The contribution to the class-203 (74.) belongs to 1.- factor and factor-2 (8.), factor-3 (1.). The contribution to the class-202 (50.) belongs to 1.- factor and factor-2 (7.), factor-3 (1.). The contribution to the class-201 (46.) belongs to 1.- factor and factor-2 (2.), factor-3 (0.). The contribution to the class-200 (8.) belongs to 1.- factor and factor-2 (7.), factor-3 (0.). The contribution to the class-199 (14.) belongs to 1.- factor and factor-2 (7.), factor-3 (2.). The contribution to the class-198 (18.) belongs to 1.- factor and factor-2 (0.), factor-3 (0.). The contribution to the class-197 (10.) belongs to 1.- factor and factor-2 (2.), factor-3 (1.). The contribution to the class-196 (13.) belongs to 1.- factor and factor-2 (1.), factor-3 (1.). The contribution to the class-195 (8.) belongs to 1.- factor and factor-2 (1.), factor-3 (1.).

Presentation of isolated classes

Significance of dipole association coefficient (class) Q(n) is the highest for the class-203 (90.) followed by: class-201 (80.), class-202 (34.).

* Inertia is 12. For the class-203 this means that it stands out most prominently, it is followed by: class-202 (9.), class-201 (7.).

* The contribution of the 1st- isolated factor to the class-203 is 74. followed by: class-202 (50.), class-201 (46.). The contribution of the 2nd- isolated factor to the class-203 is 8. followed by: class-202 (7.), class-201 (2.). The contribution of the 3rd- isolated factor to the class-203 is 1. followed by: class-202 (1.), class-201 (0.).

*, factor-3 (1.), factor-3 (1.), factor-3 (1.), factor-3 (1.), factor-3 (0.), factor-3 (0.), factor-2 (7.), factor-3 (0.), factor-3 (1.), factor-3 (1.), factor-3 (1.).

Structure of 3 isolated factor for anthropometric and linear hepatic measurements

Table 139 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

407

1000

BMI

-243

784

1000

D-il

102

461

411

1000

ApBo

163

564

494

471

1000

TvBo

194

628

548

342

597

1000

MxAp

205

515

403

384

472

396

1000

MxCo

107

158

-16

1000

MxCr

140

274

191

307

244

203

101

251

1000

MxCc

159

392

302

391

318

289

226

916

1000

Comx

151

226

155

122

335

301

192

719

267

324

1000

Vcal

204

443

334

369

387

380

507

665

726

731

610

1000

We found the strongest correlations (916) between Max CC (MxCc) and Maximal Crainocaudal (MxCr) . The strongest negative correlation is -243 between BMI (BMI) and height (hgt).

Table 140 The characteristic square of a factor and the percentage contribution

sqare

sum

4.867

40.556

2.046

17.051

57.607

1.316

10.964

68.571

1.174

9.782

78.353

.724

6.030

84.383

.625

5.212

89.596

.548

4.570

94.165

.373

3.107

97.272

.248

2.068

99.340

.070

.581

99.921

.007

.057

99.978

.003

.022

100.000

Percentage representation of the characteristic squares fall in the range between .022% and 40.556%. The new structure is consisted of 3 isolated factors which contain 68.571 % information from the whole sample.

Table 141 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

142

283

-80

236

wgt

788

779

606

125

416

173

BMI

648

638

407

489

239

117

-41

D-il

486

597

356

272

-237

ApBo

621

696

484

100

344

118

134

TvBo

631

683

466

325

106

243

MxAp

495

595

354

348

121

142

MxCo

842

404

163

-682

465

227

462

214

163

MxCr

943

634

402

-444

197

-586

343

261

MxCc

930

724

524

108

-338

114

-540

292

222

Comx

798

557

310

-491

241

118

497

247

188

Vcal

905

845

713

147

-437

191

-18

12.0

1000

The isolated factors structure for anthropometric and linear hepatic measurements

* Decreased communality shows that the structure of 3 isolated factors does not contain enough information about 1 anthropometric and linear hepatic measurement: height (hgt) 142

The variables that contribute in forming the structure of each isolated factor are: Maximal Crainocaudal, Max CC, liver volume (calculated by formula), Maximal Coronal, Cormax LL, weight, BMI, Transverse body dimension, AP body dimension, Maximal Ap, Diaphragm to iliac, the variable that does not contribute to factors structure is: height.

* Structure of the 2nd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: Maximal Coronal (MxCo) with factor contribution (cor) 465.

* Several factors contribute to variable for: Maximal Crainocaudal, factor-1 (403), factor-3 (344), Max CC, factor-1 (525), factor-3 (292).

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

Analysis of the sample consisting of 103 examinees revealed that in forming the structure of 3 isolated factors 58 (56.31%) examinees had high contribution, 23 (22.33%) examinees had intermediate contribution, with low contribution without significance were 22 (21.36%).

1. – for 36 (34.95%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure is 17 (16.50%). For 23 we found direct proportionality, and for 30 are inversely related.

3. – for 6 (5.83%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure5 (4.85%). For 7 we found direct proportionality, and for 4 are inversely related.

Concordance of anthropometric and linear hepatic measurements with the structure: one factor have 57 examinees, latent agreement only have 24 examinees, with no agreement are 22 examinees .

It should be noted that 5 examinees stands out from the rest (inr)

Graph 45 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 46 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 47 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 48 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Table 142 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-0,::GrpD-0

.10

::GrpD-0,::GrpD-0

.13

::GrpD-0,::GrpD-0

.15

::GrpD-2,::GrpD-0

.19

::GrpD-0,::GrpD-0

.25

::GrpD-2,::GrpD-3

.27

::GrpD-2,::GrpD-0

.47

::GrpD-0,::GrpD-0

.69

::GrpD-1,::GrpD-0

.71

::GrpD-1,::GrpD-0

1.55

::GrpD-1,::GrpD-2

2.35

From the dendrogram shown we found that the closest were groups ::GrpD-0 and: GrpD-0 with the distance 10. The biggest difference is between::GrpD-1 and:GrpD-2, with the distance 2.35.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3) ;;GrpD-0;; (4) ;;GrpD-0;; (5) ;;GrpD-0;; (6) ;;GrpD-0;; (7) ;;GrpD-0;; (8) ;;GrpD-0;; (9) ;;GrpD-0;; (10) ;;GrpD-0;; (11) ;;GrpD-0;; (12)

The mutual contribution of the division classes and factors structure for anthropometric and linear hepatic measurements

Table 143 Mutual contributions among division groups (3) and isolated factors structure

1-factor

2-factor

3-factor

mass

inr

kvl

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

::GrpD-1

320

1000

1862

997

228

-27

-89

::GrpD-2

301

1000

-927

247

-1614

748

383

-132

::GrpD-3

379

1000

-838

288

1306

699

316

181

As shown in Table 143 we found that the highest weight was 379. for the class ;;GrpD-3;; This means that the biggest part of the sample which belongs to one class, belongs to this class which corresponds to the specified weighting factor, and the next is for the class: ;;GrpD-1;; (320.), ;;GrpD-2;; (301.).

* Inertia (inr) of the class ;;GrpD-1;; is 93 it means that this class stands out from the rest, and the next is for class: ;;GrpD-2;; (87.), ;;GrpD-3;; (77.).

* Relative contribution (cor) 1. – of the axis to the class ;;GrpD-1;; is 997. high, which means that the axis has the most information about that class, then for: ;;GrpD-3;; (288.-low), ;;GrpD-2;; (247.-without significance). Relative contribution 2. – of the axis to the class ;;GrpD-2;; is 748. high, then for: ;;GrpD-3;; (699.-high), ;;GrpD-1;; (0.-without significance). Relative contribution 3. – of the axis to the class ;;GrpD-3;; is 13. without significance, then for: ;;GrpD-2;; (5.-without significance), ;;GrpD-1;; (2.-without significance).

* Relative contribution of the class ;;GrpD-1;; to inertia of the 1st – axis is 228., then for: ;;GrpD-3;; (55.), ;;GrpD-2;; (53.). Relative contribution of the class ;;GrpD-2;; to inertia of the 2nd – axis is 383, then for: ;;GrpD-3;; (316.), ;;GrpD-1;; (0.). Relative contribution of the class ;;GrpD-3;; inertia 3. – axis is 9, then for: ;;GrpD-2;; (4.), ;;GrpD-1;; (2.).

* Association of the classes on the 1st – axis is inversely proportional for the classes ;;GrpD-3;;, ;;GrpD-2;;, and inversely proportional for the classes, ;;GrpD-2;;, ;;GrpD-1;;, and inversely proportional for the classes, ;;GrpD-2;;, ;;GrpD-1;;.

Table 144 Contribution of each factor to a class in ‰:

::GrpD-1

997

::GrpD-2

247

748

::GrpD-3

288

699

* The factor F1 gives the highest contribution to the class ::GrpD-1 (997 :‰:) then F3 (2‰) which contributes 498.5 times less.

Table 145 Mahalanobis distance between ;;GrpD;; in relation to anthropometric and linear hepatic measurements

::GrpD-1

::GrpD-2

::GrpD-3

::GrpD-1

.00

2.55

2.30

::GrpD-2

2.55

.00

3.78

::GrpD-3

2.30

3.78

.00

By calculating the Mahalanobis distance between ;; GrpD ;; we obtained another indicator of similarities or differences. Distances of different spaces can be compared.According to the results in the table we can say that the distance is minimal between ;;GrpD;;: ;;GrpD-3;; and ;;GrpD-1;; (::GrpD-3 and:GrpD-1 (2.30) (bigger) . The farthest are;;GrpD;; : ;;GrpD-3;; and ;;GrpD-2;; (::GrpD-3 and:GrpD-2 (3.78) (bigger).

Table 146 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-1,::GrpD-3

2.30

::GrpD-1,::GrpD-2

3.23

From the dendrogram shown we found that the closest were groups ::GrpD-1 and: GrpD-3 with the distance2.30. The biggest difference is between::GrpD-1 and:GrpD-2, with the distance 3.23.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3)

Clusterisation for each age group

Analysis of the structure anthropometric and linear hepatic measurements

In accordance to the previously established design of the study, it was planned to extract optimal number of factors from a sample of 50 examinees, using factor analysis of principal components , on the basis of 12 anthropometric and linear hepatic measurements: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal). The aim is to find the associations between individual variables, to determine the contribution of each factor to a variable, contribution of each variable to a factor, to apply complementary analyses and to present the results Graphically. The coordinates of the variables for anthropometric and linear hepatic measurements will be presented to determine their position in an isolated structure.

Structure 3 isolated factor anthropometric and linear hepatic measurements

Table 1 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

515

1000

BMI

891

1000

D-il

378

503

386

1000

ApBo

271

695

662

386

1000

TvBo

303

818

791

445

816

1000

MxAp

225

636

620

457

659

623

1000

MxCo

135

-71

-34

-79

1000

MxCr

264

388

300

173

384

287

447

1000

MxCc

285

469

388

291

472

382

591

949

1000

Comx

195

-29

-10

-54

-133

916

1000

Vcal

303

523

443

240

469

482

616

614

709

751

541

1000

We found the strongest correlations (949) between Max CC (MxCc) and Maximal Crainocaudal (MxCr). The strongest negative correlation is -133 between Cormax LL (Comx) and Maximal Ap (MxAp).

Table 2 The characteristic square of a factor and the percentage contribution

sqare

sum

5.530

46.083

2.326

19.380

65.463

1.455

12.129

77.592

1.046

8.714

86.306

.610

5.087

91.393

.427

3.561

94.954

.355

2.961

97.915

.129

1.076

98.991

.083

.688

99.679

.032

.263

99.942

.005

.042

99.984

.002

.016

100.000

Percentage representation of the characteristic squares fall in the range between .016% do 46.083%. The new structure is consisted of 3 isolated factors which contain 77.592 % information from the whole.

Table 3 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

239

451

204

145

-121

wgt

884

880

775

140

-155

-291

BMI

760

783

613

111

-257

-285

D-il

393

545

297

-214

-225

ApBo

723

802

643

116

-245

-141

TvBo

849

829

687

124

-166

-367

134

MxAp

708

802

643

116

-235

102

MxCo

950

172

925

856

368

-255

MxCr

938

659

435

167

689

475

327

MxCc

966

751

565

102

106

625

390

268

Comx

949

149

915

837

360

-300

Vcal

952

786

618

112

542

294

126

198

12.0

1000

The isolated factors structure for anthropometric and linear hepatic measurements

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

Analysis of the sample consisting of 50 examinees revealed that in forming the structure of 3 isolated factors 33 (66.00%) examinees had high contribution, 12 (24.00%) examinees had intermediate contribution, with low contribution without significance were 5 (10.00%).

1. – for 17 (34.00%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 4 (8.00%). For 8 we found direct proportionality, and 13 were inversely related.

2. – for 11 (22.00%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure4 (8.00%). For 7 we found direct proportionality, and 8 examinees were inversely related.

It should be noted that 1 examinee stands out from the rest (inr)

Clustering on factors for anthropometric and linear hepatic measurements

In this part of the study we clusterised 50 examinees based on 3 isolated factors from 12 anthropometric and linear hepatic measurements

Sum of the levels of measures1.159

Table 5 Levels of grouping on the isolated factors

class

distance

class1

class2

nbr.elemn.

465

194

111

Group-1 (knot 94) that contains 16 examinees, is consisted of sublevels, knots 90 and 86 and the distance between them is 48. Group-2 (knot 96) contains 13 examinees, is consisted of sublevels, knots 91 and 95 and distance between them is 87. Group-3 (knot 97) contains 21 examinees, is consisted of sublevels, knots 93 and 83 the distance between them is 112.

Mutual contributions of hierarchical classification classes and isolated factor structures for anthropometric and linear hepatic measurements

In this part of the study we analysed 11 higher classes of hierarchical classification and 3 isolated classes from the sample consisting of 50 examinees in relation to 3 isolated factors structure for the anthropometric and linear hepatic measurements. Isolated classes are: 94, 96, 97.

Centers of hierarchical classification classes and isolated factors

Table 6 Centers of 3 hierarchical classification classes in relation to 3 isolated factors structures

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qlt

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

1000

903

740

624

-146

-718

164

198

420

422

222

1037

-1257

131

285

-142

260

318

317

416

2043

284

467

-562

140

204

571

2343

314

139

2048

240

253

-547

320

218

403

-1699

353

167

-10

643

380

263

250

460

-1339

216

293

-267

100

114

487

2239

366

-1230

110

-388

120

122

644

-1832

276

2038

341

214

-581

160

175

700

-2985

677

258

-275

470

280

152

305

-176

-1378

292

229

-223

As shown in Table() we found that the highest weight was 420. for isolated class-97 This means that the biggest part of the sample which belongs to one class, belongs to this class which corresponds to the specified weighting factor, it is followed by: class-94 (320.), class-96 (260.).

* Inertia is 903. For the class-99 this means that it stands out most prominently, it is followed by: class-98 (624.), class-97 (422.), class-96 (318.), class-93 (263.), class-94 (218.), class-95 (204.), class-90 (175.), class-89 (152.), class-91 (122.), class-92 (114.).

* Contribution of isolated factors 700. is high, for class-90 this means that isolated factors gives the most information to this class, then for: class-91 (644.-high), class-95 (571.-intermediate), class-92 (487.-intermediate), class-94 (403.-intermediate), class-96 (317.-low), class-89 (305.-low), class-93 (250.-without significance), class-97 (222.-without significance), class-98 (57.-without significance), class-99 (0.-without significance).

* Association of the cluster for the 1st- factors structure is proportional between classes-99, class-94, class-98, class-97, class-99, inversely proportional with, class-97, class-96, class-95, class-93, class-92.

* Association of the cluster for the 2nd- factors structure is proportional between classes-99, class-97, class-92, class-93, class-89, class-97, class-99, inversely proportional with, class-96, class-95, class-91.

* Association of the cluster for the 3rd- factors structure is proportional between classes-99, class-94, class-97, inversely proportional with, class-97, class-96, class-95, class-93, class-92, class-91, class-89.

Table 7 Center of hierarchical classification classes in relation to the factors axis 1 (factor variance: 5.5300)

knot

knot1

knot2

weight

inr

dst

(F1)2

acor

cor

ctr

cos

+cos2

1000

903

10841

740

624

10117

-146

-46

420

422

12048

1037

1076

452

299

260

318

14693

416

173

109

140

204

17468

2343

5489

768

314

139

561

314

320

218

8188

-1699

2887

924

353

167

-594

353

380

263

8310

460

211

160

100

114

13712

2239

5012

501

366

605

366

120

122

12183

-1832

3358

403

276

-525

276

160

175

13152

-2985

8907

1425

677

258

-823

677

280

152

6501

-176

-69

As shown in Table 7 the greatest distance (dst) is 17468. between the center of the cloud and the center of the class 95, it is followed by: class-96 (14693.), class-92 (13712.), class-90 (13152.), class-91 (12183.), class-97 (12048.), class-99 (10841.), class-98 (10117.), class-93 (8310.), class-94 (8188.), class-89 (6501.).

* The cosine of an angle (cos) -823. between the radius of the center of the class -90 and axis, class-92 (605.), class-94 (-594.), class-95 (561.), class-91 (-525.), class-97 (299.), class-93 (160.), class-96 (109.), class-89 (-69.), class-98 (-46.), class-99 (0.).

Table 8 Center of hierarchical classification classes in relation to the factors axis 2 (factor variance: 2.3256)

knot

knot1

knot2

weight

inr

dst

(F2)2

acor

cor

ctr

cos

+cos2

1000

903

10841

740

624

10117

-718

515

381

164

-226

420

422

12048

-1257

1580

664

131

285

-362

220

260

318

14693

2043

4175

1086

284

467

533

296

140

204

17468

2048

4195

587

240

253

490

554

320

218

8188

-10

-4

353

380

263

8310

-1339

1793

681

216

293

-465

241

100

114

13712

-1230

1512

151

110

-332

476

120

122

12183

2038

4152

498

341

214

584

616

160

175

13152

-275

-76

683

280

152

6501

-1378

1900

532

292

229

-541

297

Table 9 Center of hierarchical classification classes in relation to the factors axis 3 (factor variance: 1.4554)

knot

knot1

knot2

weight

inr

dst

(F3)2

acor

cor

ctr

cos

+cos2

1000

903

10841

740

624

10117

198

420

422

12048

-142

-41

222

260

318

14693

-562

316

-147

317

140

204

17468

-547

299

-131

571

320

218

8188

643

413

132

225

403

380

263

8310

-267

-93

250

100

114

13712

-388

151

-105

487

120

122

12183

-581

337

-166

644

160

175

13152

470

221

130

700

280

152

6501

-223

-88

305

* Absolute contribution (acor) 132. class-94 followed by absolute contribution for: class-96 (82.), class-95 (42.), class-91 (40.), class-90 (35.), class-98 (29.), class-93 (27.), class-92 (15.), class-89 (14.), class-97 (8.), class-99 (0.).

Analysis of differences between two nodes (dipoles) of hierarchical classification classes

Table 10 Dipoles of the 11 highest nodes in relation to the factors axes from 1 to 3

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qld

cod

ctd

cod

ctd

cod

ctd

1000

3522

-562

131

-2761

3153

631

760

239

740

9038

-2736

7007

246

1247

1455

121

784

576

420

12724

-6062

11924

241

-861

241

-1313

560

260

12899

-4175

12898

204

-10

-34

140

3263

-288

-2723

3176

-345

320

11672

-2571

11006

-530

467

-346

199

380

12811

-2414

12704

-149

165

100

4424

-506

144

2364

3150

1416

1130

120

6272

-1851

4089

-1350

2175

-75

160

4821

187

-1195

3166

-844

1578

280

7776

1090

5756

-603

1764

-230

257

As shown in Table 10 we found that Inertia of the dipole (ind) a(n) b(n) is 39, that is, the inertia of the whole system , class-99 , followed by dipoles: class-98 (16.), class-97 (9.), class-96 (7.), class-95 (6.), class-94 (4.), class-93 (3.), class-92 (2.), class-91 (2.), class-90 (1.), class-89 (1.).

* Projection ab on the axis 1st-isolated factor, that is, the projection of the dipole class-97 is -6062, other dipole projections on the axis are: class-96 (-4175.), class-98 (-2736.), class-94 (-2571.), class-93 (-2414.), class-91 (-1851.), class-89 (1090.), class-99 (-562.), class-92 (-506.), class-95 (-288.), class-90 (187.). Projection ab on the axis 2nd-isolated factor, that is, the projection of the dipole class-99 is -2761, other dipole projections on the axis are: class-95 (-2723.), class-92 (2364.), class-91 (-1350.), class-98 (1247.), class-90 (-1195.), class-97 (-861.), class-89 (-603.), class-94 (-530.), class-93 (-149.), class-96 (-10.). Projection ab on the axis 3rd-isolated factor, that is, the projection of the dipole class-92 is 1416, other dipole projections on the axis are: class-97 (-1313.), class-90 (-844.), class-98 (784.), class-99 (760.), class-94 (-346.), class-95 (-345.), class-89 (-230.), class-93 (165.), class-91 (-75.), class-96 (-34.).

* Relative contribution of the 1st-factor axis (D1), dipole a(n) b(n) of the class-96 is 12898. -high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-93 (12704.-high), class-97 (11924.-high), class-94 (11006.-high), class-98 (7007.-high), class-89 (5756.-high), class-91 (4089.-high), class-92 (144.-without significance), class-99 (131.-without significance), class-90 (78.-without significance), class-95 (36.-without significance). Relative contribution of the 2nd-factor axis (D2), dipole a(n) b(n) is class-95 is 3176. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-90 (3166.-high), class-99 (3153.-high), class-92 (3150.-high), class-91 (2175.-high), class-89 (1764.-high), class-98 (1455.-high), class-94 (467.-intermediate), class-97 (241.-without significance), class-93 (48.-without significance), class-96 (0.-without significance). Relative contribution of the 3rd-factor axis (D3), dipole a(n) b(n) is class-90 is 1578. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-92 (1130.-high), class-98 (576.-intermediate), class-97 (560.-intermediate), class-89 (257.-without significance), class-99 (239.-without significance), class-94 (199.-without significance), class-93 (59.-without significance), class-95 (51.-without significance), class-91 (7.-without significance), class-96 (1.-without significance).

* Relative contribution of dipoles (ctd) class-98 to axis of the 1st-factor is 7007, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-97 (11924.), class-96 (12898.), class-94 (11006.), class-93 (12704.), class-91 (4089.), class-89 (5756.), class-99 (131.), class-92 (144.), class-95 (36.), class-90 (78.). Relative contribution of dipoles (ctd) class-99 to axis of the 2nd-factor is 3153, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-98 (1455.), class-95 (3176.), class-92 (3150.), class-90 (3166.), class-91 (2175.), class-97 (241.), class-89 (1764.), class-94 (467.), class-93 (48.), class-96 (0.). Relative contribution of dipoles (ctd) class-98 to axis of the 3rd-factor is 576, which represents the inertia of the dipole (a(n) b(n)) on the factor axes, other inertias are: class-99 (239.), class-97 (560.), class-92 (1130.), class-90 (1578.), class-94 (199.), class-89 (257.), class-95 (51.), class-93 (59.), class-96 (1.), class-91 (7.).

Table 11 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 1

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

192

465

-562

316

131

-361

131

182

262

-2736

7487

1360

7007

246

-2647

7007

266

-6062

36753

1330

11924

241

-3453

11924

336

-4175

17432

1126

12898

204

-3591

12898

476

-288

-189

150

-2571

6610

529

11006

-3317

11006

-2414

5829

430

12704

-3564

12704

284

-506

256

144

-380

144

186

-1851

3427

4089

-2022

4089

106

187

279

1090

1187

5756

2399

5756

As shown in Table 11 the greatest distance (dst) 476. between the center of the cloud and the center of the class-95, it is followed by: class-99 (465.), class-96 (336.), class-92 (284.), class-97 (266.), class-98 (262.), class-91 (186.), class-94 (150.), class-90 (106.), class-93 (89.), class-89 (52.).

Table 12 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 2

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

192

465

-2761

7624

1467

3153

631

-1776

3284

182

262

1247

1555

282

1455

121

1206

8462

266

-861

742

241

-491

12164

336

-10

-9

12898

476

-2723

7416

212

3176

-1782

3212

150

-530

281

467

-684

11473

-149

-219

12752

284

2364

5588

3150

1775

3294

186

-1350

1823

2175

-1475

6265

106

-1195

1428

3166

-1779

3244

-603

364

1764

-1328

7520

Table 13 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 3

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

192

465

760

577

111

239

489

3522

182

262

784

615

112

576

759

9038

266

-1313

1725

560

-748

12724

336

-34

-29

12899

476

-345

119

-226

3263

150

-346

120

199

-446

11672

165

244

12811

284

1416

2005

1130

1063

4424

186

-75

-82

6272

106

-844

712

1578

-1256

4821

-230

257

-507

7776

Table 14 Relative mutual contributions of factors (from 1 to 3) per classes

kls

knot1

knot2

Q(n)

inr

+inr

192

122

182

113

111

Significance of dipole association coefficient (class) Q(n) is the highest for the class-99 (192.) followed by: class-98 (182.), class-94 (80.), class-93 (74.), class-89 (70.), class-96 (65.), class-90 (38.), class-97 (36.), class-95 (29.), class-91 (27.), class-92 (16.).

* Inertia is 39. For the class-99 this means that it stands out most prominently, it is followed by: class-98 (16.), class-97 (9.), class-96 (7.), class-95 (6.), class-94 (4.), class-93 (3.), class-92 (2.), class-91 (2.), class-90 (1.), class-89 (1.).

* The contribution of the 1st- isolated factor to the class-98 is 113, this means that examinees that belong to a class-98 have anthropometric and linear hepatic measurements characteristics of the 1st-factor structure, followed by: class-97 (111.), class-96 (94.), class-94 (44.), class-93 (36.), class-91 (8.), class-89 (7.), class-99 (5.), class-95 (0.), class-92 (0.), class-90 (0.). The contribution of the 2nd- isolated factor to the class-99 is 122. followed by: class-98 (24.), class-95 (18.), class-92 (7.), class-91 (4.), class-90 (4.), class-97 (2.), class-94 (2.), class-89 (2.), class-96 (0.), class-93 (0.). The contribution of the 3rd- isolated factor to the class-99 is 9. followed by: class-98 (9.), class-97 (5.), class-92 (3.), class-90 (2.), class-94 (1.), class-96 (0.), class-95 (0.), class-93 (0.), class-91 (0.), class-89 (0.).

*The highest contribution of the factor to the class-99 (122.) has the 1st- factor, this means that mentioned structure have examinees of the observed class. The same can be said, with less contribution, for characteristics: factor-2 (9.), factor-3 (5.). The contribution to the class-98 (113.) belongs to 1.- factor and factor-2 (24.), factor-3 (9.). The contribution to the class-97 (111.) belongs to 1.- factor and factor-2 (5.), factor-3 (2.). The contribution to the class-96 (94.) belongs to 1.- factor and factor-2 (0.), factor-3 (0.). The contribution to the class-95 (18.) belongs to 1.- factor and factor-2 (0.), factor-3 (0.). The contribution to the class-94 (44.) belongs to 1.- factor and factor-2 (2.), factor-3 (1.). The contribution to the class-93 (36.) belongs to 1.- factor and factor-2 (0.), factor-3 (0.). The contribution to the class-92 (7.) belongs to 1.- factor and factor-2 (3.), factor-3 (0.). The contribution to the class-91 (8.) belongs to 1.- factor and factor-2 (4.), factor-3 (0.). The contribution to the class-90 (4.) belongs to 1.- factor and factor-2 (2.), factor-3 (0.). The contribution to the class-89 (7.) belongs to 1.- factor and factor-2 (2.), factor-3 (0.).

Presentation of isolated classes

Significance of dipole association coefficient (class) Q(n) is the highest for the class-94 (80.) followed by: class-96 (65.), class-97 (36.).

* Inertia is 9 for the class-97 this means that it stands out most prominently, it is followed by: class-96 (7.), class-94 (4.).

* The contribution of the 1st- isolated factor to the class-97 is 111. followed by: class-96 (94.), class-94 (44.). The contribution of the 2nd- isolated factor to the class-97 is 2. followed by: class-94 (2.), class-96 (0.). The contribution of the 3rd- isolated factor to the class-97 is 5. followed by: class-94 (1.), class-96 (0.).

*, factor-2 (9.), factor-3 (9.), factor-2 (5.), factor-3 (0.), factor-3 (0.), factor-3 (1.), factor-3 (0.), factor-2 (3.), factor-3 (0.), factor-2 (2.), factor-3 (0.).

Structure of 3 isolated factors for anthropometric and linear hepatic measurements

Table 15 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

515

1000

BMI

891

1000

D-il

378

503

386

1000

ApBo

271

695

662

386

1000

TvBo

303

818

791

445

816

1000

MxAp

225

636

620

457

659

623

1000

MxCo

135

-71

-34

-79

1000

MxCr

264

388

300

173

384

287

447

1000

MxCc

285

469

388

291

472

382

591

949

1000

Comx

195

-29

-10

-54

-133

916

1000

Vcal

303

523

443

240

469

482

616

614

709

751

541

1000

We found the strongest correlations (949) between Max CC (MxCc) and Maximal Crainocaudal (MxCr). The strongest negative correlation is -133 between Cormax LL (Comx) and Maximal Ap (MxAp).

Table 16 The characteristic square of a factor and the percentage contribution

sqare

sum

5.530

46.083

2.326

19.380

65.463

1.455

12.129

77.592

1.046

8.714

86.306

.610

5.087

91.393

.427

3.561

94.954

.355

2.961

97.915

.129

1.076

98.991

.083

.688

99.679

.032

.263

99.942

.005

.042

99.984

.002

.016

100.000

Table 17 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

239

451

204

145

-121

wgt

884

880

775

140

-155

-291

BMI

760

783

613

111

-257

-285

D-il

393

545

297

-214

-225

ApBo

723

802

643

116

-245

-141

TvBo

849

829

687

124

-166

-367

134

MxAp

708

802

643

116

-235

102

MxCo

950

172

925

856

368

-255

MxCr

938

659

435

167

689

475

327

MxCc

966

751

565

102

106

625

390

268

Comx

949

149

915

837

360

-300

Vcal

952

786

618

112

542

294

126

198

12.0

1000

The isolated factors structure anthropometric and linear hepatic measurements

In forming the structure of two and more factors contribute3 anthropometric and linear hepatic measurements, in forming only one factor contribute 8 anthropometric and linear hepatic measurements, with low contribution without significance in forming the factor is 1 anthropometric and linear hepatic measurement. In forming the structure of isolated factors contribute 11 (91.67%) anthropometric and linear hepatic measurements.

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

3. – for 5 (10.00%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure are 4 (8.00%) examinees. For 5 examinees we found direct proportionality, and 4 examinees are inversely related.

It should be noted that 1 examinee stands out from the rest (inr)

Graph 5 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 6 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 7 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 8 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Table 18 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-0,::GrpD-0

.05

::GrpD-2,::GrpD-0

.09

::GrpD-0,::GrpD-0

.13

::GrpD-3,::GrpD-0

.15

::GrpD-2,::GrpD-3

.20

::GrpD-2,::GrpD-0

.38

::GrpD-2,::GrpD-0

.50

::GrpD-1,::GrpD-0

.61

::GrpD-1,::GrpD-0

1.00

::GrpD-1,::GrpD-0

1.80

::GrpD-1,::GrpD-2

2.50

From the dendrogram shown we found that the closest were groups ::GrpD-0 and:GrpD-0 with the distance.05. The biggest difference is between::GrpD-1 and:GrpD-2, distance 2.50.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3) ;;GrpD-0;; (4) ;;GrpD-0;; (5) ;;GrpD-0;; (6) ;;GrpD-0;; (7) ;;GrpD-0;; (8) ;;GrpD-0;; (9) ;;GrpD-0;; (10) ;;GrpD-0;; (11) ;;GrpD-0;; (12)

The mutual contribution of the division classes and factors structure anthropometric and linear hepatic measurements

Table 19 Mutual contributions among division groups (3) and isolated factors structure

1-factor

2-factor

3-factor

mass

inr

kvl

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

::GrpD-1

320

1000

-1699

875

167

-10

643

125

::GrpD-2

260

101

1000

416

2043

895

467

-562

::GrpD-3

420

1000

1037

402

-1257

591

285

-142

As shown in Table 19 we found that the highest weight was 420. for class ;;GrpD-3;; This means that the biggest part of the sample which belongs to one class, belongs to this class which corresponds to the specified weighting factor, and the next is for the class: ;;GrpD-1;; (320.), ;;GrpD-2;; (260.).

* Inertia (inr) of the class ;;GrpD-2;; is 101it means that this class stands out from the rest, and the next is for class: ;;GrpD-3;; (94.), ;;GrpD-1;; (88.).

* Relative contribution (cor) 1. – of the axis to the class ;;GrpD-1;; is 875. high, which means that the axis has the most information about that class, then for: ;;GrpD-3;; (402.-intermediate), ;;GrpD-2;; (37.-without significance). Relative contribution 2. – of the axis to the class ;;GrpD-2;; is 895. high, then for: ;;GrpD-3;; (591.-intermediate), ;;GrpD-1;; (0.-without significance). Relative contribution 3. – of the axis to the class ;;GrpD-1;; is 125. without significance, then for: ;;GrpD-2;; (68.-without significance), ;;GrpD-3;; (8.-without significance).

* Relative contribution of the class ;;GrpD-1;; to inertia of the 1st – axis is 167., then for: ;;GrpD-3;; (82.), ;;GrpD-2;; (8.). Relative contribution of the class ;;GrpD-2;; to inertia of the 2nd – axis is 467, then for: ;;GrpD-3;; (285.), ;;GrpD-1;; (0.). Relative contribution of the class ;;GrpD-1;; to inertia of the 3rd – axis is 91, then for: ;;GrpD-2;; (56.), ;;GrpD-3;; (6.).

* The association of classes on the 2nd axis is proportional for the classes ;;GrpD-1;;, ;;GrpD-3;;, and inversely proportional for the class, ;;GrpD-2;;.

Table 20 Contribution of each factor to a class in ‰:

::GrpD-1

875

125

::GrpD-2

895

::GrpD-3

402

591

* The factor F1 gives the highest contribution to the class ::GrpD-1 (875‰) then F3 (125‰) which 7.0 times contribute less.

Table 21 Mahalanobis distance between ;;GrpD;; in relation to anthropometric and linear hepatic measurements

::GrpD-1

::GrpD-2

::GrpD-3

::GrpD-1

.00

3.29

2.38

::GrpD-2

3.29

.00

4.59

::GrpD-3

2.38

4.59

.00

By calculating the Mahalanobis distance between ;; GrpD ;; we obtained another indicator of similarities or differences. Distances of different spaces can be compared. According to the results in the table we can say that the distance is minimal between ;;GrpD;;: ;;GrpD-3;; and ;;GrpD-1;; (::GrpD-3 and:GrpD-1 (2.38) (bigger). The farthest are;;GrpD;; : ;;GrpD-3;; and ;;GrpD-2;; (::GrpD-3 and:GrpD-2 (4.59) (bigger).

Table 22 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-1,::GrpD-3

2.38

::GrpD-1,::GrpD-2

4.17

From the dendrogram shown we found that the closest were groups ::GrpD-1 and: GrpD-3 with the distance2.38.The biggest difference is between::GrpD-1 and:GrpD-2, distance 4.17.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3)

Analysis of the structure anthropometric and linear hepatic measurements

In accordance to the previously established design of the study, it was planned to extract optimal number of factors from a sample consisting of 106, using factor analysis of principal components, from 12 anthropometric and linear hepatic measurements: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal). The aim is to find the associations between individual variables, to determine the contribution of each factor to a variable, contribution of each variable to a factor, to apply complementary analyses and to present the results Graphically. The coordinates of the variables for anthropometric and linear hepatic measurements will be presented to determine their position in an isolated structure.

Structure of 3 isolated factors anthropometric and linear hepatic measurements

Table 23 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

373

1000

BMI

-466

621

1000

D-il

-46

455

459

1000

ApBo

-54

599

597

469

1000

TvBo

677

564

524

851

1000

MxAp

385

363

320

491

473

1000

MxCo

136

-76

-37

-75

1000

MxCr

238

-74

113

146

113

1000

MxCc

225

190

256

176

214

283

926

1000

Comx

149

160

233

193

735

105

150

1000

Vcal

204

251

100

284

235

292

557

609

658

676

514

1000

We found the strongest correlations (926) between Max CC (MxCc) and Maximal Crainocaudal (MxCr). The strongest negative correlation is -466 between BMI (BMI) and height (hgt).

Table 24 The characteristic square of a factor and the percentage contribution

sqare

sum

4.191

34.925

2.638

21.985

56.910

1.623

13.523

70.433

1.225

10.205

80.638

.772

6.430

87.068

.567

4.729

91.796

.495

4.123

95.920

.277

2.311

98.230

.133

1.110

99.340

.058

.484

99.824

.017

.145

99.969

.004

.031

100.000

Table 25 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

228

-142

445

198

-96

wgt

623

-738

544

130

-280

BMI

716

-591

349

-600

360

136

D-il

475

-654

427

102

-200

ApBo

766

-752

566

135

-447

199

-15

TvBo

784

-805

649

155

-363

131

MxAp

477

-650

422

101

-125

-199

MxCo

894

-256

556

309

117

721

520

320

MxCr

887

-426

181

656

430

163

-525

276

170

MxCc

895

-564

318

562

316

120

-511

261

161

Comx

837

-389

151

436

190

704

495

305

Vcal

871

-705

497

119

609

371

140

12.0

1000

The isolated factors structure for anthropometric and linear hepatic measurements

* Decreased communality shows that the structure of 3 isolated factors does not contain enough information about 1 anthropometric and linear hepatic measurement: height (hgt) 228

The variables that contribute in forming the structure of each isolated factor are: Max CC, Maximal Coronal, Maximal Crainocaudal, liver volume (calculated by formula), Cormax LL, Transverse body dimension, AP body dimension, BMI, weight, Maximal Ap, Diaphragm to iliac, the variable that do not contribute to factors structure is: height.

* Structure of the 1st- isolated factor is formed of 6 anthropometric and linear hepatic measurements: Transverse body dimension (TvBo) with factor contribution (cor) 649, AP body dimension (ApBo) 567, weight (wgt) 544, liver volume (calculated by formula) (Vcal) 498, Diaphragm to iliac (D-il) 428, Maximal Ap (MxAp) 423. Latent variables are: BMI (BMI) 349, Max CC (MxCc) 319. Association Transverse body dimension is in concordance with: AP body dimension, weight, liver volume (calculated by formula), Diaphragm to iliac, Maximal Ap, BMI, Max CC.

* Structure of the 2nd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: Maximal Crainocaudal (MxCr) with factor contribution (cor) 431. Latent variables are: liver volume (calculated by formula) (Vcal) 371, BMI (BMI) 360, Max CC (MxCc) 316, Maximal Coronal (MxCo) 309. Association Maximal Crainocaudal is in concordance with: liver volume (calculated by formula), Max CC, Maximal Coronal. Association Maximal Crainocaudal is inversely proportional with: BMI.

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

The analysis of the sample consisting of 106 revealed that in forming the structure of 3 isolated factors 70 (66.04%) examinees had high contribution, intermediate contribution had 23 (21.70%) examinees, with low contribution , without significance were 13 (12.26%) examinees.

1. – for 43 (40.57%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 16 (15.09%) examinees. For 24 examinees we found direct proportionality, and for 35 examinees are inversely related.

2. – for 17 (16.04%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure are 10 (9.43%) examinees. For 13 examinees we found direct proportionality, and for 14 examinees are inversely related.

3. – for 10 (9.43%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure are 10 (9.43%) examinees. For 11 examinees we found direct proportionality, and 9 examinees are inversely related.

Concordance of anthropometric and linear hepatic measurements with the structure: two and more factor have 1, one factor have 68, latent agreement only have 24 , with no agreement are 13 .

It should be noted that 1 examinee stands out from the rest (inr)

Graph 9 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 10 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 11 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 12 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Clustering on factors for anthropometric and linear hepatic measurements

In this part of the study we clusterised 106 based on 3 isolated factors from 12 anthropometric and linear hepatic measurements

Sum of the levels of measures1.152

Table 27 Levels of grouping on the isolated factors

class

distance

class1

class2

nbr.elemn.

211

449

210

208

106

210

239

209

207

209

203

206

208

205

204

207

202

198

206

197

196

205

201

194

204

199

193

203

184

200

202

190

195

201

174

189

200

179

192

Group-1 (knot 207) contain 22 , is consisted of sublevels, knots 202 and 198 the distance between them is 54. Group-2 (knot 208) contain 45 , is consisted of sublevels, knots 205 and 204 the distance between them is 71. Group-3 (knot 209) contain 39, is consisted of sublevels, knots 203 and 206 the distance between them is 85.

Mutual contributions of hierarchical classification classes and isolated factor structures for anthropometric and linear hepatic measurements

Centers of hierarchical classification classes and isolated factors

Table 28 Centers of 3 hierarchical classification classes in relation to 3 isolated factors structures

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qlt

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

211

210

208

1000

904

210

209

207

575

592

171

-1446

170

287

-104

-45

209

203

206

368

369

301

-1457

176

186

-1225

125

209

-55

208

205

204

425

350

391

1960

389

141

207

202

198

208

242

398

-1427

145

101

1883

253

279

-27

206

197

196

132

211

568

-3079

494

299

-1191

205

201

194

104

137

600

2526

402

158

1718

186

116

-437

204

199

193

321

218

409

1778

387

242

-369

222

203

184

200

236

165

221

-549

-1244

184

138

-88

202

190

195

183

603

-2311

229

120

2887

358

298

608

201

174

189

725

3308

645

172

1039

-520

As shown in Table 28 we found that the highest weight was 425. for isolated class-208. This means that the biggest part of the sample which belongs to one class, belongs to this class which corresponds to the specified weighting factor, it is followed by: class-209 (368.), class-207 (208.).

* Inertia is 904 for the class-211, this means that it stands out most prominently, it is followed by: class-210 (592.), class-209 (369.), class-208 (350.), class-207 (242.), class-204 (218.), class-206 (211.), class-202 (183.), class-203 (165.), class-205 (137.), class-201 (93.).

* Relative contribution of the 1st-isolated factor to the center of the class-201 is 645. high, this means that factor gives the most information to this class, then for: center of the class-206 (494.-intermediate), center of the class-205 (402.-intermediate), center of the class-208 (389.-low), center of the class-204 (387.-low), center of the class-202 (229.-without significance), center of the class-209 (176.-without significance), center of the class-210 (170.-without significance), center of the class-207 (145.-without significance), center of the class-203 (36.-without significance), center of the class-211 (0.-without significance). Relative contribution of the 2nd-isolated factor to the center of the class-202 is 358. low, then for: center of the class-207 (253.-without significance), center of the class-205 (186.-without significance), center of the class-203 (184.-without significance), center of the class-209 (125.-without significance), center of the class-206 (74.-without significance), center of the class-201 (64.-without significance), center of the class-204 (17.-without significance), center of the class-208 (2.-without significance), center of the class-210 (1.-without significance), center of the class-211 (0.-without significance). Relative contribution of the 3rd-isolated factor to the center of the class-202 is 16. without significance, then for: center of the class-201 (16.-without significance), center of the class-205 (12.-without significance), center of the class-204 (6.-without significance), center of the class-203 (1.-without significance), center of the class-211 (0.-without significance), center of the class-210 (0.-without significance), center of the class-209 (0.-without significance), center of the class-208 (0.-without significance), center of the class-207 (0.-without significance), center of the class-206 (0.-without significance).

Table 29 Center of hierarchical classification classes in relation to the factors axis 1 (factor variance: 4.1910)

knot

knot1

knot2

weight

inr

dst

(F1)2

acor

cor

ctr

cos

+cos2

211

210

208

1000

904

10848

210

209

207

575

592

12336

-1446

2092

1204

170

287

-412

170

209

203

206

368

369

12042

-1457

2123

781

176

186

-420

176

208

205

204

425

350

9889

1960

3844

1632

389

624

389

207

202

198

208

242

14008

-1427

2036

423

145

101

-381

145

206

197

196

132

211

19194

-3079

9479

1252

494

299

-703

494

205

201

194

104

137

15881

2526

6381

662

402

158

634

402

204

199

193

321

218

8170

1778

3160

1013

387

242

622

387

203

184

200

236

165

8399

-549

301

-190

202

190

195

183

23289

-2311

5341

504

229

120

-479

229

201

174

189

16963

3308

10942

723

645

172

803

645

As shown in Table 29 the greatest distance (dst) 23289. between the center of the cloud and the center of the class-202, it is followed by: class-206 (19194.), class-201 (16963.), class-205 (15881.), class-207 (14008.), class-210 (12336.), class-209 (12042.), class-211 (10848.), class-208 (9889.), class-203 (8399.), class-204 (8170.).

* Absolute contribution (acor) 1632. class-208 followed by absolute contribution for: class-206 (1252.), class-210 (1204.), class-204 (1013.), class-209 (781.), class-201 (723.), class-205 (662.), class-202 (504.), class-207 (423.), class-203 (71.), class-211 (0.).

Table 30 Center of hierarchical classification classes in relation to the factors axis 2 (factor variance: 2.6383)

knot

knot1

knot2

weight

inr

dst

(F2)2

acor

cor

ctr

cos

+cos2

211

210

208

1000

904

10848

210

209

207

575

592

12336

-104

-30

170

209

203

206

368

369

12042

-1225

1500

552

125

209

-353

301

208

205

204

425

350

9889

141

391

207

202

198

208

242

14008

1883

3544

736

253

279

503

398

206

197

196

132

211

19194

-1191

1419

187

-272

568

205

201

194

104

137

15881

1718

2951

306

186

116

431

588

204

199

193

321

218

8170

-369

136

-129

403

203

184

200

236

165

8399

-1244

1547

365

184

138

-429

220

202

190

195

183

23289

2887

8336

786

358

298

598

587

201

174

189

16963

1039

1079

252

709

Table 31 Center of hierarchical classification classes in relation to the factors axis 3 (factor variance: 1.6228)

knot

knot1

knot2

weight

inr

dst

(F3)2

acor

cor

ctr

cos

+cos2

211

210

208

1000

904

10848

210

209

207

575

592

12336

-45

-13

171

209

203

206

368

369

12042

-55

-16

301

208

205

204

425

350

9889

391

207

202

198

208

242

14008

-27

-7

398

206

197

196

132

211

19194

568

205

201

194

104

137

15881

-437

191

-110

600

204

199

193

321

218

8170

222

409

203

184

200

236

165

8399

-88

-31

221

202

190

195

183

23289

608

369

126

603

201

174

189

16963

-520

271

-126

725

Analysis of differences between two nodes (dipoles) of hierarchical classification classes

Table 32 Dipoles of the 11 highest nodes in relation to the factors axes from 1 to 3

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qld

cod

ctd

cod

ctd

cod

ctd

211

210

208

1000

6352

-3407

6313

677

-245

-105

210

209

207

575

5358

-30

-3108

5357

486

-27

209

203

206

368

6360

2530

6349

129

-53

-94

208

205

204

425

5937

749

622

2087

4833

129

-659

482

207

202

198

208

7045

-1621

2510

1842

3240

1164

1294

206

197

196

132

5438

676

290

2841

5113

-237

205

201

194

104

5920

2150

3352

-1868

2530

-229

204

199

193

321

7220

-795

1823

1151

3820

-739

1577

203

184

200

236

7093

-887

2145

1140

3548

716

1400

202

190

195

9619

-1818

4165

-1210

1845

-1692

3610

201

174

189

6399

1290

2343

-1550

3382

693

675

As shown in Table 32 we found that Inertia of the dipole (ind) a(n) b(n) is 37, that is, the inertia of the whole system , class-211 , followed by dipoles: class-210 (20.), class-209 (7.), class-208 (6.), class-207 (4.), class-206 (3.), class-205 (3.), class-204 (2.), class-203 (2.), class-202 (2.), class-201 (1.).

Table 33 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 1

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

211

210

208

244

449

-3407

11606

2835

6313

677

-2513

6313

210

209

207

133

416

-30

-23

209

203

206

232

2530

6400

542

6349

129

2520

6349

208

205

204

166

749

560

622

789

622

207

202

198

260

-1621

2628

135

2510

-1584

2510

206

197

196

266

676

457

290

538

290

205

201

194

319

2150

4623

111

3352

1831

3352

204

199

193

-795

632

1823

-1350

1823

203

184

200

-887

786

2145

-1465

2145

202

190

195

198

-1818

3305

4165

-2041

4165

201

174

189

174

1290

1664

2343

1531

2343

As shown in Table 33 the greatest distance (dst) 449. between the center of the cloud and the center of the class-211 , it is followed by: class-210 (416.), class-205 (319.), class-206 (266.), class-207 (260.), class-209 (232.), class-202 (198.), class-201 (174.), class-208 (166.), class-203 (90.), class-204 (76.).

Table 34 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 2

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

211

210

208

244

449

-245

-181

6346

210

209

207

133

416

-3108

9657

1281

5357

486

-2315

5358

209

203

206

232

-53

-52

6352

208

205

204

166

2087

4355

341

4833

129

2198

5455

207

202

198

260

1842

3392

175

3240

1800

5751

206

197

196

266

2841

8069

179

5113

2261

5403

205

201

194

319

-1868

3489

2530

-1591

5882

204

199

193

1151

1324

3820

1955

5643

203

184

200

1140

1300

3548

1884

5693

202

190

195

198

-1210

1464

1845

-1358

6010

201

174

189

174

-1550

2403

3382

-1839

5724

Table 35 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 3

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

211

210

208

244

449

-105

-78

6352

210

209

207

133

416

-27

-20

5358

209

203

206

232

-94

-93

6360

208

205

204

166

-659

434

482

-694

5937

207

202

198

260

1164

1355

1294

1138

7045

206

197

196

266

-237

-188

5438

205

201

194

319

-229

-195

5920

204

199

193

-739

547

1577

-1256

7220

203

184

200

716

513

1400

1183

7093

202

190

195

198

-1692

2864

3610

-1900

9619

201

174

189

174

693

480

675

822

6399

Table 36 Relative mutual contributions of factors (from 1 to 3) per classes

kls

knot1

knot2

Q(n)

inr

+inr

211

210

208

244

236

210

209

207

133

107

209

203

206

208

205

204

207

202

198

206

197

196

205

201

194

204

199

193

203

184

200

202

190

195

201

174

189

* Inertia is 37 for the class-211 this means that it stands out most prominently, it is followed by: class-210 (20.), class-209 (7.), class-208 (6.), class-207 (4.), class-206 (3.), class-205 (3.), class-204 (2.), class-203 (2.), class-202 (2.), class-201 (1.).

Presentation of isolated classes

Significance of dipole association coefficient (class) Q(n) is the highest for the class-209 (85.) followed by: class-208 (78.), class-207 (51.).

* Inertia 7. class-209 this means that it stands out most prominently, it is followed by: class-208 (6.), class-207 (4.).

*, factor-3 (0.), factor-3 (0.), factor-3 (0.), factor-3 (3.), factor-3 (6.), factor-3 (0.), factor-3 (0.), factor-3 (3.), factor-3 (2.), factor-2 (6.), factor-3 (1.).

Structure 3 isolated factor anthropometric and linear hepatic measurements

Table 37 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

373

1000

BMI

-466

621

1000

D-il

-46

455

459

1000

ApBo

-54

599

597

469

1000

TvBo

677

564

524

851

1000

MxAp

385

363

320

491

473

1000

MxCo

136

-76

-37

-75

1000

MxCr

238

-74

113

146

113

1000

MxCc

225

190

256

176

214

283

926

1000

Comx

149

160

233

193

735

105

150

1000

Vcal

204

251

100

284

235

292

557

609

658

676

514

1000

We found the strongest correlations (926) between Max CC (MxCc) and Maximal Crainocaudal (MxCr) . The strongest negative correlation is -466 between BMI (BMI) and height (hgt).

Table 38 The characteristic square of a factor and the percentage contribution

sqare

sum

4.191

34.925

2.638

21.985

56.910

1.623

13.523

70.433

1.225

10.205

80.638

.772

6.430

87.068

.567

4.729

91.796

.495

4.123

95.920

.277

2.311

98.230

.133

1.110

99.340

.058

.484

99.824

.017

.145

99.969

.004

.031

100.000

Table 39 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

228

-142

445

198

-96

wgt

623

-738

544

130

-280

BMI

716

-591

349

-600

360

136

D-il

475

-654

427

102

-200

ApBo

766

-752

566

135

-447

199

-15

TvBo

784

-805

649

155

-363

131

MxAp

477

-650

422

101

-125

-199

MxCo

894

-256

556

309

117

721

520

320

MxCr

887

-426

181

656

430

163

-525

276

170

MxCc

895

-564

318

562

316

120

-511

261

161

Comx

837

-389

151

436

190

704

495

305

Vcal

871

-705

497

119

609

371

140

12.0

1000

The factor structure for anthropometric and linear hepatic measurements

* Decreased communality shows that the structure of 3 isolated factors does not contain enough information about 1 anthropometric and linear hepatic measurement: height (hgt) 228

* Structure of the 1st- isolated factor is formed of 6 anthropometric and linear hepatic measurements: Transverse body dimension (TvBo) with factor contribution (cor) 649, AP body dimension (ApBo) 567, weight (wgt) 544, liver volume (calculated by formula) (Vcal) 498, Diaphragm to iliac (D-il) 428, Maximal Ap (MxAp) 423. Latent variables are: BMI (BMI) 349, Max CC (MxCc) 319. Association Transverse body dimension is in concordance with: AP body dimension, weight, liver volume (calculated by formula), Diaphragm to iliac, Maximal Ap, BMI, Max CC.

* Structure of the 2nd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: Maximal Crainocaudal (MxCr) with factor contribution (cor) 431. Latent variables are: liver volume (calculated by formula) (Vcal) 371, BMI (BMI) 360, Max CC (MxCc) 316, Maximal Coronal (MxCo) 309. Association Maximal Crainocaudal is in concordance with: liver volume (calculated by formula), Max CC, Maximal Coronal. Association Maximal Crainocaudal is inversely proportional with: BMI.

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

The analysis of the sample consisting of 106 revealed that in forming the structure of 3 isolated factors have high contribution70 (66.04%), intermediate contribution 23 (21.70%), with low contribution , without significance are 13 (12.26%).

Concordance anthropometric and linear hepatic measurements with the structure: two and more factor have 1 , one factor have 68 , latent agreement only have 24 , with no agreement are 13 .

It should be noted that 1 examinee stands out from the rest (inr)

Graph 13 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 14 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 15 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 16 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Table 40 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-2,::GrpD-0

.12

::GrpD-2,::GrpD-0

.16

::GrpD-0,::GrpD-0

.17

::GrpD-0,::GrpD-0

.18

::GrpD-2,::GrpD-0

.23

::GrpD-2,::GrpD-0

.41

::GrpD-2,::GrpD-3

.46

::GrpD-1,::GrpD-0

.60

::GrpD-1,::GrpD-0

.74

::GrpD-1,::GrpD-0

1.69

::GrpD-1,::GrpD-2

3.34

From the dendrogram shown we found that the closest were groups ::GrpD-2 and:GrpD-0 with the distance.12.The biggest difference is between::GrpD-1 and: GrpD-2, with the distance 3.34.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3) ;;GrpD-0;; (4) ;;GrpD-0;; (5) ;;GrpD-0;; (6) ;;GrpD-0;; (7) ;;GrpD-0;; (8) ;;GrpD-0;; (9) ;;GrpD-0;; (10) ;;GrpD-0;; (11) ;;GrpD-0;; (12)

The mutual contribution of the division classes and factors structure anthropometric and linear hepatic measurements

Table 41 Mutual contributions among division groups (3) and isolated factors structure

1-factor

2-factor

3-factor

mass

inr

kvl

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

::GrpD-1

208

1000

-1427

365

101

1883

635

279

-27

::GrpD-2

425

137

1000

1960

994

389

141

::GrpD-3

368

111

1000

-1457

585

186

-1225

414

209

-55

* Inertia (inr) of the class ;;GrpD-2;; is 137 it means that this class stands out from the rest, and the next is for classes: ;;GrpD-3;; (111.), ;;GrpD-1;; (97.).

* Relative contribution of the class ;;GrpD-2;; inertia 1. – axis is389., then for: ;;GrpD-3;; (186.), ;;GrpD-1;; (101.). Relative contribution of the class ;;GrpD-1;; to to inertia of the 2nd – axis is279, then for: ;;GrpD-3;; (209.), ;;GrpD-2;; (3.). Relative contribution of the class ;;GrpD-2;; inertia 3. – axis is 1, then for: ;;GrpD-3;; (1.), ;;GrpD-1;; (0.).

*, and inversely proportional for classes ;;GrpD-3;;, ;;GrpD-1;;. The association of classes on the 2nd axis is proportional for the classes ;;GrpD-2;;, ;;GrpD-1;;, and inversely proportional for the class, ;;GrpD-3;;, and inversely proportional for the class, ;;GrpD-3;;, ;;GrpD-1;;.

Table 42 Contribution of each factor to a class in ‰:

::GrpD-1

365

635

::GrpD-2

994

::GrpD-3

585

414

* To the class ::GrpD-1 the highest contribution gives F2 factor (635 :‰:) then F1 (365 ‰) which contribute 1.7 times less.

Table 43 Mahalanobis distance between ;;GrpD;; in relation to anthropometric and linear hepatic measurements

::GrpD-1

::GrpD-2

::GrpD-3

::GrpD-1

.00

3.06

2.68

::GrpD-2

3.06

.00

3.34

::GrpD-3

2.68

3.34

.00

By calculating the Mahalanobis distance between ;; GrpD ;; we obtained another indicator of similarities or differences. Distances of different spaces can be compared. According to the results in table we can say that the distance is minimal between ;;GrpD;;: ;;GrpD-3;; and ;;GrpD-1;; (::GrpD-3 and:GrpD-1 (2.68) (bigger) . The farthest are;;GrpD;; : ;;GrpD-3;; and ;;GrpD-2;; (::GrpD-3 and:GrpD-2 (3.34) (bigger).

Table 44 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-1,::GrpD-3

2.68

::GrpD-1,::GrpD-2

3.29

From the dendrogram shown we found that the closest were groups ::GrpD-1 and: GrpD-3 with the distance 2.68.The biggest difference is between::GrpD-1 and:GrpD-2, distance 3.29.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3)

Analysis of the structure of anthropometric and linear hepatic measurements

In accordance to the previously established design of the study, it was planned to extract optimal number of factors from a sample of 98 examinees using factor analysis of principal components, from 12 anthropometric and linear hepatic measurements: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal). The aim is to find the associations between individual variables, to determine the contribution of each factor to a variable, contribution of each variable to a factor, to apply complementary analyses and to present the results Graphically. The coordinates of the variables for anthropometric and linear hepatic measurements will be presented to determine their position in an isolated structure.

Structure 3 isolated factor anthropometric and linear hepatic measurements

Table 45 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

507

1000

BMI

-95

807

1000

D-il

227

402

305

1000

ApBo

122

668

687

328

1000

TvBo

215

659

611

381

801

1000

MxAp

162

297

227

202

517

353

1000

MxCo

-110

-40

163

-25

1000

MxCr

215

308

186

253

307

209

233

1000

MxCc

217

433

328

396

408

363

306

118

903

1000

Comx

211

288

178

267

197

314

621

159

232

1000

Vcal

174

341

247

341

455

351

635

489

737

750

427

1000

We found the strongest correlations (903) between Max CC (MxCc) and Maximal Crainocaudal (MxCr) . The strongest negative correlation is -110 between Maximal Coronal (MxCo) and height (hgt).

Table 46 The characteristic square of a factor and the percentage contribution

sqare

sum

4.846

40.387

1.871

15.594

55.982

1.481

12.345

68.327

1.178

9.818

78.144

.936

7.804

85.948

.708

5.898

91.847

.433

3.610

95.456

.302

2.517

97.973

.158

1.314

99.287

.078

.648

99.935

.006

.051

99.986

.002

.014

100.000

Percentage representation of the characteristic squares fall in the range between .014% do 40.387%. The new structure is consisted of 3 isolated factors which contain 68.327 % information from the whole.

Table 47 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

166

-343

118

-217

wgt

812

-789

623

129

430

185

BMI

744

-662

439

504

254

136

228

D-il

323

-557

310

-28

110

ApBo

785

-794

631

130

385

148

TvBo

759

-751

564

116

377

142

231

MxAp

363

-553

306

-237

MxCo

882

-233

-634

402

215

653

426

288

MxCr

858

-639

408

-423

179

-520

271

183

MxCc

852

-758

575

119

-340

116

-402

162

109

Comx

751

-455

207

-408

166

614

378

255

Vcal

902

-782

611

126

-526

276

148

-118

12.0

1000

The isolated factors structure for anthropometric and linear hepatic measurements

* Several factors contribute to variable for: Maximal Coronal, factor-2 (402), factor-3 (427), liver volume (calculated by formula), factor-1 (612), factor-2 (277).

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

The analysis of the sample consisting of 98 examinees revealed that in forming the structure of 3 isolated factors 50 (51.02%) examinees had high contribution, intermediate contribution had 23 (23.47%), with low contribution , without significance were 25 (25.51%) examinees.

1. – for 36 (36.73%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure were 10 (10.20%) examinees. For 23 we found direct proportionality, and 23 examinees are inversely related.

2. – for 11 (11.22%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure were 8 (8.16%) examinees. For 9 examinees we found direct proportionality, and 10 examinees were inversely related.

3. – for 10 (10.20%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure4 (4.08%). For 8 examinees we found direct proportionality, and 6 examinees were inversely related.

Concordance anthropometric and linear hepatic measurements with the structure: two and more factor have 1 , one factor have 55 , latent agreement only have 15 , with no agreement are 27 .

It should be noted that 1 examinee stands out from the rest (inr)

Graph 17 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 18 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 19 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 20 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Clustering on factors for anthropometric and linear hepatic measurements

In this part of the study we clusterised 98 examinees based on 3 isolated factors from 12 anthropometric and linear hepatic measurements

Sum of the levels of measures1.050

Table 49 Levels of grouping on the isolated factors

class

distance

class1

class2

nbr.elemn.

195

322

192

194

227

190

193

126

191

189

192

187

186

191

172

188

190

185

189

183

178

188

184

180

187

179

173

186

176

181

185

175

182

184

174

165

Group-1 (knot 190) contain 18 , is consisted of sublevels, knots 27 and 185 the distance between them is 37. Group-2 (knot 192) contain 28 , is consisted of sublevels, knots 187 and 186 the distance between them is 74. Group-3 (knot 193) contain 52, is consisted of sublevels, knots 191 and 189 the distance between them is 127.

Mutual contributions of hierarchical classification classes and isolated factor structures anthropometric and linear hepatic measurements

Centers of hierarchical classification classes and isolated factors

Table 50 Centers of 3 hierarchical classification classes in relation to 3 isolated factors structures

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qlt

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

195

192

194

1000

913

194

190

193

714

699

-194

-609

142

193

191

189

531

418

149

881

-791

177

192

187

186

286

241

253

485

1522

229

354

-43

191

172

188

173

203

303

391

-1969

276

359

478

190

185

184

300

558

-3298

555

412

-83

-198

189

183

178

357

225

173

1119

165

-219

-96

188

184

180

153

167

238

-1680

215

231

483

187

179

173

652

-1859

226

2470

399

233

648

186

176

181

214

156

359

1266

184

1206

167

-273

185

175

182

173

231

553

-2968

552

315

-160

As shown in Table 50 we found that the highest weight was 531. for isolated class-193. This means that the biggest part of the sample which belongs to one class, belongs to this class which corresponds to the specified weighting factor, it is followed by: class-192 (286.), class-190 (184.).

* Inertia is 913. For the class-195 this means that it stands out most prominently, it is followed by: class-194 (699.), class-193 (418.), class-190 (300.), class-192 (241.), class-185 (231.), class-189 (225.), class-191 (203.), class-188 (167.), class-186 (156.), class-187 (91.).

* Contribution of isolated factors 652. is high, for class-187 this means that isolated factors gives the most information to this class, then for: class-190 (558.-intermediate), class-185 (553.-intermediate), class-186 (359.-low), class-191 (303.-low), class-192 (253.-without significance), class-188 (238.-without significance), class-189 (173.-without significance), class-193 (149.-without significance), class-194 (35.-without significance), class-195 (0.-without significance).

Table 51 Center of hierarchical classification classes in relation to the factors axis 1 (factor variance: 4.8465)

knot

knot1

knot2

weight

inr

dst

(F1)2

acor

cor

ctr

cos

+cos2

195

192

194

1000

913

10950

194

190

193

714

699

11737

-194

-57

193

191

189

531

418

9446

881

776

412

287

192

187

186

286

241

10113

485

235

152

191

172

188

173

203

14032

391

153

104

190

185

184

300

19590

-3298

10877

1998

555

412

-745

555

189

183

178

357

225

7573

1119

1252

447

165

407

165

188

184

180

153

167

13098

238

187

179

173

15298

-1859

3456

247

226

-475

226

186

176

181

214

156

8729

1266

1602

343

184

429

184

185

175

182

173

231

15958

-2968

8807

1528

552

315

-743

552

* Absolute contribution (acor) 1998. class-190 followed by absolute contribution for: class-185 (1528.), class-189 (447.), class-193 (412.), class-186 (343.), class-187 (247.), class-192 (67.), class-194 (27.), class-191 (26.), class-188 (9.), class-195 (0.).

Table 52 Center of hierarchical classification classes in relation to the factors axis 2 (factor variance: 1.8713)

knot

knot1

knot2

weight

inr

dst

(F2)2

acor

cor

ctr

cos

+cos2

195

192

194

1000

913

10950

194

190

193

714

699

11737

-609

371

265

142

-178

193

191

189

531

418

9446

-791

625

332

177

-257

148

192

187

186

286

241

10113

1522

2317

662

229

354

479

252

191

172

188

173

203

14032

-1969

3876

672

276

359

-526

287

190

185

184

300

19590

-83

-19

556

189

183

178

357

225

7573

-219

-80

172

188

184

180

153

167

13098

-1680

2822

432

215

231

-464

220

187

179

173

15298

2470

6100

436

399

233

632

625

186

176

181

214

156

8729

1206

1455

312

167

408

350

185

175

182

173

231

15958

552

* Absolute contribution (acor) 672. class-191 followed by absolute contribution for: class-192 (662.), class-187 (436.), class-188 (432.), class-193 (332.), class-186 (312.), class-194 (265.), class-189 (17.), class-190 (1.), class-195 (0.), class-185 (0.).

Table 53 Center of hierarchical classification classes in relation to the factors axis 3 (factor variance: 1.4814)

knot

knot1

knot2

weight

inr

dst

(F3)2

acor

cor

ctr

cos

+cos2

195

192

194

1000

913

10950

194

190

193

714

699

11737

193

191

189

531

418

9446

149

192

187

186

286

241

10113

-43

-14

253

191

172

188

173

203

14032

478

228

128

303

190

185

184

300

19590

-198

-45

558

189

183

178

357

225

7573

-96

-35

173

188

184

180

153

167

13098

483

234

134

238

187

179

173

15298

648

420

166

652

186

176

181

214

156

8729

-273

-93

359

185

175

182

173

231

15958

-160

-40

553

* The cosine of an angle (cos) 166. between the radius of the center of the class -187 and axis, class-188 (134.), class-191 (128.), class-186 (-93.), class-190 (-45.), class-185 (-40.), class-189 (-35.), class-193 (30.), class-192 (-14.), class-194 (5.), class-195 (0.).

Analysis of differences between two nodes (dipoles) of hierarchical classification classes

Table 54 Dipoles of the 11 highest nodes in relation to the factors axes from 1 to 3

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qld

cod

ctd

cod

ctd

cod

ctd

195

192

194

1000

3169

678

291

2131

2875

495

-60

194

190

193

714

10837

-4179

10486

492

708

301

-289

193

191

189

531

3618

-728

489

-1750

2825

191

574

304

192

187

186

286

8864

-3125

7088

108

1263

1159

922

617

191

172

188

173

3525

1298

770

-2455

2754

-48

190

185

184

9888

-5948

9124

-1581

645

-679

119

189

183

178

357

10887

2129

10292

392

350

329

246

188

184

180

153

10981

3034

10384

538

326

-489

270

187

179

173

3828

-1357

907

2351

2720

640

202

186

176

181

214

4846

-857

2394

-848

2344

-181

107

185

175

182

173

10280

-1500

5557

-791

1546

-1134

3178

As shown in Table 54 we found that Inertia of the dipole (ind) a(n) b(n) is 27, that is, the inertia of the whole system , class-195 , followed by dipoles: class-194 (19.), class-193 (11.), class-192 (6.), class-191 (3.), class-190 (3.), class-189 (3.), class-188 (3.), class-187 (2.), class-186 (1.), class-185 (1.).

* Relative contribution of the 1st-factor axis (D1), dipole a(n) b(n) is class-194 is 10486. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-188 (10384.-high), class-189 (10292.-high), class-190 (9124.-high), class-192 (7088.-high), class-185 (5557.-high), class-186 (2394.-high), class-187 (907.-high), class-191 (770.-high), class-193 (489.-intermediate), class-195 (291.-low). Relative contribution of the 2nd-factor axis (D2), dipole a(n) b(n) is class-195 is 2875. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-193 (2825.-high), class-191 (2754.-high), class-187 (2720.-high), class-186 (2344.-high), class-185 (1546.-high), class-192 (1159.-high), class-190 (645.-high), class-189 (350.-low), class-188 (326.-low), class-194 (301.-low). Relative contribution of the 3rd-factor axis (D3), dipole a(n) b(n) is class-185 is 3178. is high, which represents the angle between the axis of the vector factor ab (dipole) other angles for: class-192 (617.-high), class-193 (304.-low), class-188 (270.-without significance), class-189 (246.-without significance), class-187 (202.-without significance), class-190 (119.-without significance), class-186 (107.-without significance), class-194 (50.-without significance), class-195 (2.-without significance), class-191 (1.-without significance).

Table 55 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 1

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

195

192

194

204

322

678

460

291

540

291

194

190

193

136

318

-4179

17462

2383

10486

492

-3238

10486

193

191

189

117

239

-728

530

489

-699

489

192

187

186

258

-3125

9764

523

7088

108

-2662

7088

191

172

188

227

1298

1685

770

877

770

190

185

203

-5948

35384

341

9124

-3021

9124

189

183

178

103

2129

4531

378

10292

3208

10292

188

184

180

213

3034

9204

338

10384

3222

10384

187

179

173

415

-1357

1842

907

-952

907

186

176

181

-857

734

2394

-1547

2394

185

175

182

-1500

2249

5557

-2357

5557

As shown in Table 55 the greatest distance (dst) 415. between the center of the cloud and the center of the class-187 , it is followed by: class-195 (322.), class-194 (318.), class-192 (258.), class-193 (239.), class-191 (227.), class-188 (213.), class-190 (203.), class-189 (103.), class-185 (84.), class-186 (68.).

Table 56 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 2

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

195

192

194

204

322

2131

4541

927

2875

495

1696

3167

194

190

193

136

318

708

501

301

548

10786

193

191

189

117

239

-1750

3063

358

2825

191

-1681

3315

192

187

186

258

1263

1596

1159

1076

8247

191

172

188

227

-2455

6028

109

2754

-1660

3524

190

185

203

-1581

2500

645

-803

9769

189

183

178

103

392

154

350

591

10641

188

184

180

213

538

289

326

571

10711

187

179

173

415

2351

5526

2720

1649

3626

186

176

181

-848

719

2344

-1531

4738

185

175

182

-791

626

1546

-1243

7102

Table 57 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 3

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

195

192

194

204

322

-60

-48

3169

194

190

193

136

318

-289

-224

10837

193

191

189

117

239

574

329

304

551

3618

192

187

186

258

922

849

617

785

8864

191

172

188

227

-48

-33

3525

190

185

203

-679

461

119

-345

9888

189

183

178

103

329

108

246

496

10887

188

184

180

213

-489

239

270

-520

10981

187

179

173

415

640

410

202

449

3828

186

176

181

-181

107

-327

4846

185

175

182

-1134

1286

3178

-1783

10280

Table 58 Relative mutual contributions of factors (from 1 to 3) per classes

kls

knot1

knot2

Q(n)

inr

+inr

195

192

194

204

194

190

193

136

199

193

191

189

117

192

187

186

191

172

188

190

185

189

183

178

188

184

180

187

179

173

186

176

181

185

175

182

Significance of dipole association coefficient (class) Q(n) is the highest for the class-195 (204.) followed by: class-194 (136.), class-193 (117.), class-189 (83.), class-192 (54.), class-186 (48.), class-188 (37.), class-185 (36.), class-191 (18.), class-187 (15.), class-190 (10.).

* Inertia 27. class-195 this means that it stands out most prominently, it is followed by: class-194 (19.), class-193 (11.), class-192 (6.), class-191 (3.), class-190 (3.), class-189 (3.), class-188 (3.), class-187 (2.), class-186 (1.), class-185 (1.).

*The highest contribution of the factor to the class-195 (77.) has the 1st- factor, this means that mentioned structure have examinees of the observed class. The same can be said, with less contribution, for characteristics: factor-2 (8.), factor-3 (0.). The contribution to the class-194 (199.) belongs to 1.- factor and factor-2 (6.), factor-3 (1.). The contribution to the class-193 (30.) belongs to 1.- factor and factor-2 (5.), factor-3 (3.). The contribution to the class-192 (44.) belongs to 1.- factor and factor-2 (7.), factor-3 (4.). The contribution to the class-191 (9.) belongs to 1.- factor and factor-2 (3.), factor-3 (0.). The contribution to the class-190 (28.) belongs to 1.- factor and factor-2 (2.), factor-3 (0.). The contribution to the class-189 (31.) belongs to 1.- factor and factor-2 (1.), factor-3 (1.). The contribution to the class-188 (28.) belongs to 1.- factor and factor-2 (1.), factor-3 (1.). The contribution to the class-187 (7.) belongs to 1.- factor and factor-2 (2.), factor-3 (0.). The contribution to the class-186 (3.) belongs to 1.- factor and factor-2 (3.), factor-3 (0.). The contribution to the class-185 (7.) belongs to 1.- factor and factor-2 (4.), factor-3 (2.).

Presentation of isolated classes

Significance of dipole association coefficient (class) Q(n) is the highest for the class-193 (117.) followed by: class-192 (54.), class-190 (10.).

* Inertia of the 11th class-193 this means that it stands out most prominently, it is followed by: class-192 (6.), class-190 (3.).

*, factor-3 (0.), factor-3 (1.), factor-3 (3.), factor-3 (4.), factor-3 (0.), factor-3 (0.), factor-3 (1.), factor-3 (1.), factor-3 (0.), factor-3 (0.), factor-2 (4.).

Structure of 3 isolated factors for anthropometric and linear hepatic measurements

Table 59 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

507

1000

BMI

-95

807

1000

D-il

227

402

305

1000

ApBo

122

668

687

328

1000

TvBo

215

659

611

381

801

1000

MxAp

162

297

227

202

517

353

1000

MxCo

-110

-40

163

-25

1000

MxCr

215

308

186

253

307

209

233

1000

MxCc

217

433

328

396

408

363

306

118

903

1000

Comx

211

288

178

267

197

314

621

159

232

1000

Vcal

174

341

247

341

455

351

635

489

737

750

427

1000

We found the strongest correlations (903) between Max CC (MxCc) and Maximal Crainocaudal (MxCr) . The strongest negative correlation is -110 between Maximal Coronal (MxCo) and height (hgt).

Table 60 The characteristic square of a factor and the percentage contribution

sqare

sum

4.846

40.387

1.871

15.594

55.982

1.481

12.345

68.327

1.178

9.818

78.144

.936

7.804

85.948

.708

5.898

91.847

.433

3.610

95.456

.302

2.517

97.973

.158

1.314

99.287

.078

.648

99.935

.006

.051

99.986

.002

.014

100.000

Table 61 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

166

-343

118

-217

wgt

812

-789

623

129

430

185

BMI

744

-662

439

504

254

136

228

D-il

323

-557

310

-28

110

ApBo

785

-794

631

130

385

148

TvBo

759

-751

564

116

377

142

231

MxAp

363

-553

306

-237

MxCo

882

-233

-634

402

215

653

426

288

MxCr

858

-639

408

-423

179

-520

271

183

MxCc

852

-758

575

119

-340

116

-402

162

109

Comx

751

-455

207

-408

166

614

378

255

Vcal

902

-782

611

126

-526

276

148

-118

12.0

1000

The factor structure for anthropometric and linear hepatic measurements

* Several factors contribute to variable for: Maximal Coronal, factor-2 (402), factor-3 (427), liver volume (calculated by formula), factor-1 (612), factor-2 (277).

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

The analysis of the sample consisting of 98 examinees revealed that in forming the structure of 3 isolated factors 50 (51.02%) examinees had high contribution, 23 (23.47%) had intermediate contribution, with low contribution , without significance were 25 (25.51%).

1. – for 36 (36.73%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 10 (10.20%) examinees. For 23 examinees we found direct proportionality, and for 23 examinees are inversely related.

2. – for 11 (11.22%) anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure are 8 (8.16%) examinees. For 9 we found direct proportionality, and 10 were inversely related.

3. – for 10 (10.20%) anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure4 (4.08%). For 8 we found direct proportionality, and for 6 were inversely related.

Concordance anthropometric and linear hepatic measurements with the structure: two and more factor have 1 examinee , one factor have 55 examinees , latent agreement only have 15 examinees, with no agreement are 27 examinees .

It should be noted that 1 examinee stands out from the rest (inr)

Graph 21 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 22 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 23 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 24 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Table 62 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-2,::GrpD-0

.05

::GrpD-3,::GrpD-0

.15

::GrpD-0,::GrpD-0

.19

::GrpD-1,::GrpD-0

.21

::GrpD-2,::GrpD-3

.27

::GrpD-0,::GrpD-0

.32

::GrpD-1,::GrpD-0

.42

::GrpD-0,::GrpD-0

.45

::GrpD-1,::GrpD-0

1.09

::GrpD-1,::GrpD-0

1.90

::GrpD-1,::GrpD-2

2.10

From the dendrogram shown we found that the closest were groups ::GrpD-2 and:GrpD-0 with the distance.05.The biggest difference is between::GrpD-1 and:GrpD-2, with the distance 2.10.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3) ;;GrpD-0;; (4) ;;GrpD-0;; (5) ;;GrpD-0;; (6) ;;GrpD-0;; (7) ;;GrpD-0;; (8) ;;GrpD-0;; (9) ;;GrpD-0;; (10) ;;GrpD-0;; (11) ;;GrpD-0;; (12)

The mutual contribution of the division classes and factors structure for anthropometric and linear hepatic measurements

Table 63 Mutual contributions among division groups (3) and isolated factors structure

1-factor

2-factor

3-factor

mass

inr

kvl

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

::GrpD-1

184

167

1000

-3298

996

412

-83

-198

::GrpD-2

286

1000

485

1522

907

354

-43

::GrpD-3

531

1000

881

550

-791

444

177

As shown in Table 63 we found that the highest weight was 531. for class ;;GrpD-3;; This means that the biggest part of the sample which belongs to one class, belongs to this class which corresponds to the specified weighting factor, and the next is for the class: ;;GrpD-2;; (286.), ;;GrpD-1;; (184.).

* Inertia (inr) of the class ;;GrpD-1;; is 167it means that this class stands out from the rest, and the next is for class: ;;GrpD-3;; (62.), ;;GrpD-2;; (61.).

* Relative contribution (cor) 1. – of the axis to the class ;;GrpD-1;; is 996. high, which means that the axis has the most information about that class, then for: ;;GrpD-3;; (550.-intermediate), ;;GrpD-2;; (92.-without significance). Relative contribution 2. – of the axis to the class ;;GrpD-2;; is 907. high, then for: ;;GrpD-3;; (444.-intermediate), ;;GrpD-1;; (1.-without significance). Relative contribution 3. – of the axis to the class ;;GrpD-3;; is 6. without significance, then for: ;;GrpD-1;; (4.-without significance), ;;GrpD-2;; (1.-without significance).

* Relative contribution of the class ;;GrpD-1;; to inertia of the 1st – axis is 412., then for: ;;GrpD-3;; (85.), ;;GrpD-2;; (14.). Relative contribution of the class ;;GrpD-2;; to inertia of the 2nd – axis is354, then for: ;;GrpD-3;; (177.), ;;GrpD-1;; (1.). Relative contribution of the class ;;GrpD-1;; to inertia of the 3rd – axis is5, then for: ;;GrpD-3;; (3.), and ;;GrpD-2;; (0.).

* The association of classes on the 2nd axis is proportional for the classes ;;GrpD-1;;, ;;GrpD-3;;, and inversely proportional for the class, ;;GrpD-2;;. Association of classes on the 3rd – axis is proportional for classes ;;GrpD-1;;, ;;GrpD-2;;, and inversely proportional for the class, ;;GrpD-3;;.

Table 64 Contribution of each factor to a class in ‰:

::GrpD-1

996

::GrpD-2

907

::GrpD-3

550

444

* The factor F1 gives the highest contribution to the class ::GrpD-1 (996 :‰:) then F3 (4‰) which contribute 249.0 times less. The factor F2 gives the highest contribution to the class ::GrpD-2 (907 :‰:) then F1 (92‰) which contribute 9.9 times less. To a class ::GrpD-3 the highest contribution gives F1 factor (550 :‰:) then F2 (444‰) which contribute 1.2 times less.

Table 65 Class and inertia of the factors axis-absolute contribution

mass

dcnt

actr1

actr2

actr3

::GrpD-1

184

10923

2001

::GrpD-2

286

2553

662

::GrpD-3

531

1409

412

332

* Absolute contribution of the class ::GrpD-1 to inertia of the 1st- axis (2001), this means mass *distance squared followed by: class ::GrpD-3 (412), class ::GrpD-2 (67). Absolute contribution of the class ::GrpD-2 inertia of the 2nd axis (662), this means mass *distance squared followed by: class ::GrpD-3 (332), class ::GrpD-1 (1). Absolute contribution of the class ::GrpD-1 inertia of the 3rd axis (7), this means mass *distance squared followed by: class ::GrpD-3 (4), class ::GrpD-2 (0). The highest absolute contribution of the class ::GrpD-1 to inertia of the axis is for the 1st- axis (2001) then for the 2nd- axis (1). The highest absolute contribution of the class ::GrpD-2 inertia of the axis is for the 2nd- axis (662) then for the 3rd- axis (0). The highest absolute contribution of the class ::GrpD-3 inertia of the axis is for the 1st- axis (412) then for the 3rd- axis (4).

Table 66 Mutual contributions of the the isolated factors structures and differences between two centers of the groups (dipoles)

1-factor

2-factor

3-factor

Group

inr

kvl

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

1890

1000

3783

846

330

1605

152

154

155

2462

1000

4179

968

492

-708

289

1026

1000

396

-2313

968

531

134

Table 67 Mahalanobis distance between ;;GrpD;; in relation to anthropometric and linear hepatic measurements

::GrpD-1

::GrpD-2

::GrpD-3

::GrpD-1

.00

2.86

2.88

::GrpD-2

2.86

.00

2.49

::GrpD-3

2.88

2.49

.00

By calculating the Mahalanobis distance between ;; GrpD ;; we obtained another indicator of similarities or differences. Distances of different spaces can be compared. According to the results in the table we can say that the distance is minimal between ;;GrpD;;: ;;GrpD-3;; and ;;GrpD-2;; (::GrpD-3 and:GrpD-2 (2.49) (bigger). The farthest are;;GrpD;; : ;;GrpD-3;; and ;;GrpD-1;; (::GrpD-3 and:GrpD-1 (2.88) (bigger).

Table 68 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-2,::GrpD-3

2.49

::GrpD-1,::GrpD-2

2.97

From the dendrogram shown we found that the closest were groups ::GrpD-2 and:GrpD-3 with the distance 2.49. The biggest difference is between::GrpD-1 and:GrpD-2, distance 2.97.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3)

Analysis of the structure anthropometric and linear hepatic measurements

In accordance to the previously established design of the study, it was planned to extract optimal number of factors from the sample of 58 examinees, using factor analysis of principal components, on the basis of 12 anthropometric and linear hepatic measurements: height (hgt), weight (wgt), BMI (BMI), Diaphragm to iliac (D-il), AP body dimension (ApBo), Transverse body dimension (TvBo), Maximal Ap (MxAp), Maximal Coronal (MxCo), Maximal Crainocaudal (MxCr), Max CC (MxCc), Cormax LL (Comx), liver volume (calculated by formula) (Vcal). The aim is to find the associations between individual variables, to determine the contribution of each factor to a variable, contribution of each variable to a factor, to apply complementary analyses and to present the results Graphically. The coordinates of the variables for anthropometric and linear hepatic measurements will be presented to determine their position in an isolated structure.

Structure 3 isolated factor anthropometric and linear hepatic measurements

Table 69 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

263

1000

BMI

-308

834

1000

D-il

-12

347

322

1000

ApBo

-50

709

729

228

1000

TvBo

712

644

267

865

1000

MxAp

619

580

423

714

647

1000

MxCo

237

161

167

-81

1000

MxCr

-90

-25

-12

1000

MxCc

-69

136

194

225

114

136

921

1000

Comx

197

183

239

140

182

868

-82

1000

Vcal

117

502

432

400

492

414

536

610

497

595

543

1000

We found the strongest correlations (921) between Max CC (MxCc) and Maximal Crainocaudal (MxCr). The strongest negative correlation is -308 between BMI (BMI) and height (hgt).

Table 70 The characteristic square of a factor and the percentage contribution

sqare

sum

4.625

38.543

2.246

18.713

57.255

2.027

16.892

74.148

1.070

8.917

83.065

.852

7.104

90.169

.512

4.266

94.435

.381

3.172

97.608

.118

.987

98.595

.106

.886

99.481

.055

.459

99.940

.006

.048

99.988

.001

.012

100.000

Percentage representation of the characteristic squares fall in the range between .012% do 38.543%. The new structure is consisted of 3 isolated factors which contain 74.148 % information from the whole sample.

Table 71 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

225

-61

301

-362

131

wgt

789

-849

722

156

-178

-188

BMI

761

-802

643

139

-341

116

D-il

263

-488

239

-135

ApBo

823

-854

730

158

-304

-19

TvBo

764

-810

656

142

-295

-145

MxAp

703

-769

591

128

-327

107

-72

MxCo

904

-281

827

684

305

-376

141

MxCr

946

-252

337

113

877

769

380

MxCc

945

-389

151

345

119

821

674

333

Comx

851

-351

123

724

524

233

-451

203

100

Vcal

924

-790

623

135

524

274

122

163

12.0

1000

The isolated factors structure for anthropometric and linear hepatic measurements

* Several factors contribute to variable for: liver volume (calculated by formula), factor-1 (624), factor-2 (275).

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

Analysis of the sample consisting of 58 examinees revealed that in forming the structure of 3 isolated factors 40 (68.97%) examinees had high contribution, 8 (13.79%) had intermediate contribution, with low contribution , without significance were 10 (17.24%) examinees.

1. – for 22 (37.93%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 4 (6.90%). For 11 examinees we found direct proportionality, and 15 examinees were inversely related.

2. – for 9 (15.52%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure are 6 (10.34%) examinees. For 9 we found direct proportionality, and 6 examinees were inversely related.

3. – for 7 (12.07%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure10 (17.24%). For 8 examinees we found direct proportionality, and for 9 examinees were inversely related.

Concordance anthropometric and linear hepatic measurements with the structure: two and more factor have 2 examinees, one factor have 34 examinees , latent agreement only have 13 , with no agreement are 9 examinees .

It should be noted that 3 examinees stand out from the rest (inr)

Graph 25 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 26 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 27 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 28 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Clustering on factors anthropometric and linear hepatic measurements

In this part of the study we clusterised 135 examinees based on 3 isolated factors from 12 anthropometric and linear hepatic measurements

Sum of the levels of measures1.269

Table 115 Levels of grouping on the isolated factors

class

distance

class1

class2

nbr.elemn.

269

399

265

268

135

268

298

262

267

105

267

168

266

263

266

264

259

265

260

257

264

258

252

263

232

261

262

253

244

261

251

250

260

248

256

259

249

255

258

254

243

Group-1 (knot 262) contain 21, is consisted of sublevels, knots 253 and 244 the distance between them is 22. Group-2 (knot 265) contain 30, is consisted of sublevels, knots 260 and 257 the distance between them is 62. Group-3 (knot 267) contain 84 , is consisted of sublevels, knots 266 and 263 the distance between them is 168.

Mutual contributions of hierarchical classification classes and isolated factor structures anthropometric and linear hepatic measurements

Centers of hierarchical classification classes and isolated factors

Table 116 Centers of 3 hierarchical classification classes in relation to 3 isolated factors structures

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qlt

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

269

265

268

1000

894

268

262

267

778

612

278

567

126

-33

267

266

263

622

419

175

1106

151

159

434

266

264

259

422

251

140

421

887

110

168

183

265

260

257

222

315

287

-974

-1984

231

442

115

264

258

252

193

146

482

1521

254

1397

214

190

353

263

232

261

200

182

630

2552

596

273

-523

-318

262

253

244

156

218

622

-3031

547

299

1098

-251

261

251

250

163

141

601

2454

579

206

-239

-409

260

248

256

104

218

376

-2495

247

135

-1784

126

167

215

259

249

255

230

112

-502

459

As shown in Table 116 we found that the highest weight was 622 for the isolated class-267 This means that the biggest part of the sample which belongs to one class, belongs to this class which corresponds to the specified weighting factor, it is followed by: class-265 (222.), class-262 (156.).

* Relative contribution of the 1st-isolated factor to the center of the class-263 is 596. intermediate, this means that factor gives the most information to this class, then for: center of the class-261 (579.-intermediate), center of the class-262 (547.-intermediate), center of the class-264 (254.-without significance), center of the class-260 (247.-without significance), center of the class-267 (151.-without significance), center of the class-265 (56.-without significance), center of the class-259 (43.-without significance), center of the class-266 (25.-without significance), center of the class-268 (8.-without significance), center of the class-269 (0.-without significance). Relative contribution of the 2nd-isolated factor to the center of the class-265 is 231. without significance, then for: center of the class-264 (214.-without significance), center of the class-260 (126.-without significance), center of the class-266 (110.-without significance), center of the class-262 (72.-without significance), center of the class-259 (36.-without significance), center of the class-268 (34.-without significance), center of the class-263 (25.-without significance), center of the class-267 (23.-without significance), center of the class-261 (5.-without significance), center of the class-269 (0.-without significance). Relative contribution of the 3rd-isolated factor to the center of the class-261 is 16. without significance, then for: center of the class-264 (14.-without significance), center of the class-263 (9.-without significance), center of the class-266 (5.-without significance), center of the class-262 (4.-without significance), center of the class-260 (2.-without significance), center of the class-265 (1.-without significance), center of the class-269 (0.-without significance), center of the class-268 (0.-without significance), center of the class-267 (0.-without significance), center of the class-259 (0.-without significance).

Table 117 Center of hierarchical classification classes in relation to the factors axis 1 (factor variance: 4.7745)

knot

knot1

knot2

weight

inr

dst

(F1)2

acor

cor

ctr

cos

+cos2

269

265

268

1000

894

10731

268

262

267

778

612

9445

278

267

266

263

622

419

8085

1106

1222

761

151

159

389

151

266

264

259

422

251

7139

421

177

158

265

260

257

222

315

17032

-974

948

211

-236

264

258

252

193

146

9100

1521

2313

446

254

504

254

263

232

261

200

182

10926

2552

6510

1302

596

273

772

596

262

253

244

156

218

16800

-3031

9188

1429

547

299

-740

547

261

251

250

163

141

10400

2454

6022

981

579

206

761

579

260

248

256

104

218

25172

-2495

6227

646

247

135

-497

247

259

249

255

230

112

5870

-502

252

-207

As shown in Table 117 the greatest distance (dst) 25172. between the center of the cloud and the center of the class-260 , it is followed by: class-265 (17032.), class-262 (16800.), class-263 (10926.), class-269 (10731.), class-261 (10400.), class-268 (9445.), class-264 (9100.), class-267 (8085.), class-266 (7139.), class-259 (5870.).

* Absolute contribution (acor) 1429. class-262 followed by absolute contribution for: class-263 (1302.), class-261 (981.), class-267 (761.), class-260 (646.), class-264 (446.), class-265 (211.), class-266 (75.), class-268 (60.), class-259 (58.), class-269 (0.).

Table 118 Center of hierarchical classification classes in relation to the factors axis 2 (factor variance: 1.9782)

knot

knot1

knot2

weight

inr

dst

(F2)2

acor

cor

ctr

cos

+cos2

269

265

268

1000

894

10731

268

262

267

778

612

9445

567

321

250

126

185

267

266

263

622

419

8085

434

188

117

153

174

266

264

259

422

251

7139

887

787

332

110

168

332

135

265

260

257

222

315

17032

-1984

3935

874

231

442

-481

287

264

258

252

193

146

9100

1397

1951

376

214

190

463

469

263

232

261

200

182

10926

-523

273

-158

621

262

253

244

156

218

16800

1098

1206

188

268

619

261

251

250

163

141

10400

-239

-74

585

260

248

256

104

218

25172

-1784

3182

330

126

167

-356

374

259

249

255

230

112

5870

459

211

190

Table 119 Center of hierarchical classification classes in relation to the factors axis 3 (factor variance: 1.5492)

knot

knot1

knot2

weight

inr

dst

(F3)2

acor

cor

ctr

cos

+cos2

269

265

268

1000

894

10731

268

262

267

778

612

9445

-33

-11

267

266

263

622

419

8085

175

266

264

259

422

251

7139

183

140

265

260

257

222

315

17032

115

287

264

258

252

193

146

9100

353

124

117

482

263

232

261

200

182

10926

-318

101

-96

630

262

253

244

156

218

16800

-251

-61

622

261

251

250

163

141

10400

-409

168

-127

601

260

248

256

104

218

25172

215

376

259

249

255

230

112

5870

Analysis of differences between two nodes (dipoles) of hierarchical classification classes

Table 120 Dipoles of the 11 highest nodes in relation to the factors axes from 1 to 3

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qld

cod

ctd

cod

ctd

cod

ctd

269

265

268

1000

3502

-1252

678

-2551

2814

568

148

268

262

267

778

7359

-4137

7143

446

664

184

-272

267

266

263

622

5463

-2131

3659

129

1410

1601

136

501

202

266

264

259

422

6158

2023

4971

938

1068

313

119

265

260

257

222

7444

-2853

7287

375

126

188

264

258

252

193

7339

1867

5592

-713

815

-762

931

263

232

261

200

3601

527

349

-1531

2948

492

304

262

253

244

156

3735

-712

880

-1254

2732

-267

123

261

251

250

163

7521

1962

7469

163

-4

260

248

256

104

5376

-594

477

-1463

2896

1217

2003

259

249

255

230

5344

-1038

3751

-670

1564

As shown in Table 120 we found that Inertia of the dipole (ind) a(n) b(n) is 33, that is, the inertia of the whole system , class-269 , followed by dipoles: class-268 (25.), class-267 (14.), class-266 (7.), class-265 (5.), class-264 (2.), class-263 (2.), class-262 (2.), class-261 (2.), class-260 (1.), class-259 (1.).

Table 121 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 1

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

269

265

268

173

400

-1252

1567

271

678

-823

678

268

262

267

124

383

-4137

17113

2130

7143

446

-2673

7143

267

266

263

136

271

-2131

4541

616

3659

129

-1913

3659

266

264

259

105

204

2023

4093

429

4971

2230

4971

265

260

257

278

-2853

8139

450

7287

-2699

7287

264

258

252

133

1867

3486

143

5592

2365

5592

263

232

261

120

527

278

349

591

349

262

253

244

144

-712

506

880

-938

880

261

251

250

128

1962

3850

156

7469

2733

7469

260

248

256

170

-594

353

477

-691

477

259

249

255

-1038

1077

3751

-1937

3751

As shown in Table 121 the greatest distance (dst) 400. between the center of the cloud and the center of the class-269 , it is followed by: class-268 (383.), class-265 (278.), class-267 (271.), class-266 (204.), class-260 (170.), class-262 (144.), class-264 (133.), class-261 (128.), class-263 (120.), class-259 (68.).

Table 122 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 2

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

269

265

268

173

400

-2551

6505

1124

2814

568

-1678

3492

268

262

267

124

383

664

441

184

429

7328

267

266

263

136

271

1410

1987

270

1601

136

1265

5261

266

264

259

105

204

938

879

1068

1033

6039

265

260

257

278

375

141

126

355

7413

264

258

252

133

-713

508

815

-903

6408

263

232

261

120

-1531

2345

2948

-1717

3297

262

253

244

144

-1254

1573

2732

-1653

3612

261

251

250

128

163

227

7521

260

248

256

170

-1463

2142

2896

-1702

3373

259

249

255

-670

449

1564

-1251

5315

Table 123 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 3

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

269

265

268

173

400

148

3502

268

262

267

124

383

-272

-176

7359

267

266

263

136

271

501

251

202

450

5463

266

264

259

105

204

313

119

344

6158

265

260

257

278

188

177

7444

264

258

252

133

-762

580

931

-965

7339

263

232

261

120

492

242

304

551

3601

262

253

244

144

-267

123

-351

3735

261

251

250

128

-4

-6

7521

260

248

256

170

1217

1481

2003

1415

5376

259

249

255

170

5344

Table 124 Relative mutual contributions of factors (from 1 to 3) per classes

kls

knot1

knot2

Q(n)

inr

+inr

269

265

268

173

268

262

267

124

177

267

266

263

136

266

264

259

105

265

260

257

264

258

252

263

232

261

262

253

244

261

251

250

260

248

256

259

249

255

* Inertia 33. class-269 this means that it stands out most prominently, it is followed by: class-268 (25.), class-267 (14.), class-266 (7.), class-265 (5.), class-264 (2.), class-263 (2.), class-262 (2.), class-261 (2.), class-260 (1.), class-259 (1.).

Presentation of isolated classes

Significance of dipole association coefficient (class) Q(n) is the highest for the class-267 (136.) followed by: class-265 (55.), class-262 (39.).

* Inertia 14. class-267 this means that it stands out most prominently, it is followed by: class-265 (5.), class-262 (2.).

*, factor-3 (0.), factor-3 (1.), factor-3 (3.), factor-3 (1.), factor-3 (0.), factor-3 (2.), factor-3 (1.), factor-3 (0.), factor-3 (0.), factor-2 (3.), factor-3 (0.).

Analysis of the structure anthropometric and linear hepatic measurements

Structure 3 isolated factor anthropometric and linear hepatic measurements

Table 125 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

407

1000

BMI

-243

784

1000

D-il

102

461

411

1000

ApBo

163

564

494

471

1000

TvBo

194

628

548

342

597

1000

MxAp

205

515

403

384

472

396

1000

MxCo

107

158

-16

1000

MxCr

140

274

191

307

244

203

101

251

1000

MxCc

159

392

302

391

318

289

226

916

1000

Comx

151

226

155

122

335

301

192

719

267

324

1000

Vcal

204

443

334

369

387

380

507

665

726

731

610

1000

We found the strongest correlations (916) between Max CC (MxCc) and Maximal Crainocaudal (MxCr) . The strongest negative correlation is -243 between BMI (BMI) and height (hgt).

Table 126 The characteristic square of a factor and the percentage contribution

sqare

sum

4.867

40.556

2.046

17.051

57.607

1.316

10.964

68.571

1.174

9.782

78.353

.724

6.030

84.383

.625

5.212

89.596

.548

4.570

94.165

.373

3.107

97.272

.248

2.068

99.340

.070

.581

99.921

.007

.057

99.978

.003

.022

100.000

Table 127 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

142

283

-80

236

wgt

788

779

606

125

416

173

BMI

648

638

407

489

239

117

-41

D-il

486

597

356

272

-237

ApBo

621

696

484

100

344

118

134

TvBo

631

683

466

325

106

243

MxAp

495

595

354

348

121

142

MxCo

842

404

163

-682

465

227

462

214

163

MxCr

943

634

402

-444

197

-586

343

261

MxCc

930

724

524

108

-338

114

-540

292

222

Comx

798

557

310

-491

241

118

497

247

188

Vcal

905

845

713

147

-437

191

-18

12.0

1000

The isolated factors structure for anthropometric and linear hepatic measurements

* Decreased communality shows that the structure of 3 isolated factors does not contain enough information about 1 anthropometric and linear hepatic measurement: height (hgt) 142

The variables that contribute in forming the structure of each isolated factor are: Maximal Crainocaudal, Max CC, liver volume (calculated by formula), Maximal Coronal, Cormax LL, weight, BMI, Transverse body dimension, AP body dimension, Maximal Ap, Diaphragm to iliac, the variables that do not contribute to factor structure are: height.

* Structure of the 2nd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: Maximal Coronal (MxCo) with factor contribution (cor) 465.

* Several factors contribute to variable for: Maximal Crainocaudal, factor-1 (403), factor-3 (344), Max CC, factor-1 (525), factor-3 (292).

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

1. – for 36 (34.95%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 17 (16.50%) examinees. For 23 examinees we found direct proportionality, and 30 examinees were inversely related.

2. – for 15 (14.56%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure are 13 (12.62%) examinees. For 14 examinees we found direct proportionality, and 14 were inversely related.

3. – for 6 (5.83%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure are 5 (4.85%) examinees. For 7 examinees we found direct proportionality, and 4 were inversely related.

Concordance anthropometric and linear hepatic measurements with the structure: one factor have 57 examinees , latent agreement only have 24 examinees , with no agreement are 22 examinees.

It should be noted that 5 examinees stands out from the rest (inr)

Graph 41 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 42 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 43 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 44 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Clustering on factors for anthropometric and linear hepatic measurements

In this part of the study we clusterised 103 examinees based on 3 isolated factors from 12 anthropometric and linear hepatic measurements

Sum of the levels of measures1.379

Table 129 Levels of grouping on the isolated factors

class

distance

class1

class2

nbr.elemn.

205

471

204

202

103

204

273

201

203

148

196

198

202

107

188

200

201

199

193

200

195

197

199

194

181

198

191

189

197

192

162

196

186

187

195

177

182

194

165

190

Group-1 (knot 201) contain 33 , is consisted of sublevels, knots 199 and 193 the distance between them is 79. Group-2 (knot 202) contain 31 , is consisted of sublevels, knots 188 and 200 the distance between them is 107. Group-3 (knot 203) contain 39 , is consisted of sublevels, knots 196 and 198 the distance between them is 149.

Mutual contributions of hierarchical classification classes and isolated factor structures for anthropometric and linear hepatic measurements

Centers of hierarchical classification classes and isolated factors

Table 130 Centers of 3 hierarchical classification classes in relation to 3 isolated factors structures

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qlt

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

205

204

202

1000

885

204

201

203

699

637

399

695

165

203

196

198

379

354

218

-838

1306

152

316

181

202

188

200

301

288

304

-927

-1614

227

383

-132

201

199

193

320

306

303

1862

303

228

-27

-89

200

195

197

262

226

405

-1472

210

117

-1408

192

254

-196

199

194

181

155

229

588

3210

582

329

-336

-35

198

191

189

233

202

483

-2053

405

202

900

197

192

162

126

107

482

-889

-2026

404

253

-86

196

186

187

146

164

385

1105

1957

283

273

387

195

177

182

136

122

447

-2013

375

113

-834

-298

* Inertia is 885. for the class-205 this means that it stands out most prominently, it is followed by: class-204 (637.), class-203 (354.), class-201 (306.), class-202 (288.), class-199 (229.), class-200 (226.), class-198 (202.), class-196 (164.), class-195 (122.), class-197 (107.).

Table 131 Center of hierarchical classification classes in relation to the factors axis 1 (factor variance: 4.8667)

knot

knot1

knot2

weight

inr

dst

(F1)2

acor

cor

ctr

cos

+cos2

205

204

202

1000

885

10621

204

201

203

699

637

10933

399

159

111

121

203

196

198

379

354

11210

-838

703

266

-250

202

188

200

301

288

11464

-927

860

259

-274

201

199

193

320

306

11460

1862

3467

1111

303

228

550

303

200

195

197

262

226

10325

-1472

2165

568

210

117

-458

210

199

194

181

155

229

17712

3210

10305

1601

582

329

763

582

198

191

189

233

202

10410

-2053

4214

982

405

202

-636

405

197

192

162

126

107

10168

-889

790

100

-279

196

186

187

146

164

13510

1105

1221

178

301

195

177

182

136

122

10805

-2013

4050

551

375

113

-612

375

As shown in Table 131 the greatest distance (dst) 17712. between the center of the cloud and the center of the class-199 , it is followed by: class-196 (13510.), class-202 (11464.), class-201 (11460.), class-203 (11210.), class-204 (10933.), class-195 (10805.), class-205 (10621.), class-198 (10410.), class-200 (10325.), class-197 (10168.).

Table 132 Center of hierarchical classification classes in relation to the factors axis 2 (factor variance: 2.0461)

knot

knot1

knot2

weight

inr

dst

(F2)2

acor

cor

ctr

cos

+cos2

205

204

202

1000

885

10621

204

201

203

699

637

10933

695

483

338

165

210

203

196

198

379

354

11210

1306

1707

646

152

316

390

215

202

188

200

301

288

11464

-1614

2606

784

227

383

-477

302

201

199

193

320

306

11460

-27

-8

303

200

195

197

262

226

10325

-1408

1982

520

192

254

-438

402

199

194

181

155

229

17712

-336

113

-80

588

198

191

189

233

202

10410

900

810

189

279

483

197

192

162

126

107

10168

-2026

4105

518

404

253

-635

481

196

186

187

146

164

13510

1957

3830

558

283

273

533

374

195

177

182

136

122

10805

-834

695

-254

439

* Absolute contribution (acor) 784. class-202 followed by absolute contribution for: class-203 (646.), class-196 (558.), class-200 (520.), class-197 (518.), class-204 (338.), class-198 (189.), class-195 (95.), class-199 (18.), class-205 (0.), class-201 (0.).

Table 133 Center of hierarchical classification classes in relation to the factors axis 3 (factor variance: 1.3156)

knot

knot1

knot2

weight

inr

dst

(F3)2

acor

cor

ctr

cos

+cos2

205

204

202

1000

885

10621

204

201

203

699

637

10933

203

196

198

379

354

11210

181

218

202

188

200

301

288

11464

-132

-39

304

201

199

193

320

306

11460

-89

-27

303

200

195

197

262

226

10325

-196

-61

405

199

194

181

155

229

17712

-35

-8

588

198

191

189

233

202

10410

483

197

192

162

126

107

10168

-86

-27

482

196

186

187

146

164

13510

387

150

105

385

195

177

182

136

122

10805

-298

-91

447

Analysis of differences between two nodes (dipoles) of hierarchical classification classes

Table 134 Dipoles of the 11 highest nodes in relation to the factors axes from 1 to 3

1 -factor

2 -factor

3 -factor

kls

knot1

knot2

weight

inr

qld

cod

ctd

cod

ctd

cod

ctd

205

204

202

1000

3181

1327

785

2310

2380

548

189

204

201

203

699

5795

2700

4621

260

-1334

1128

151

-270

203

196

198

379

6754

3158

6012

184

1057

674

336

202

188

200

301

6486

4216

5602

124

-1601

807

493

201

199

193

320

7334

2617

6957

113

-599

365

106

200

195

197

262

3924

-1124

1816

1192

2044

-212

199

194

181

155

9160

-2404

5439

-956

861

1743

2860

198

191

189

233

7853

2022

7726

-246

114

197

192

162

126

6305

2037

5063

898

983

-460

259

196

186

187

146

7758

2103

6974

-478

360

519

425

195

177

182

136

7486

-1766

5847

-623

727

697

911

* The quality of the observed factors (qld) 9160. is high, for class-199 (dipole) which represents the quality of the vector ab representation in the factors space of this research, the other qualities are for: class-198 (7853.-high), class-196 (7758.-high), class-195 (7486.-high), class-201 (7334.-high), class-203 (6754.-high), class-202 (6486.-high), class-197 (6305.-high), class-204 (5795.-high), class-200 (3924.-high), class-205 (3181.-high).

Table 135 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 1

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

205

204

202

210

472

1327

1760

370

785

886

785

204

201

203

174

392

2700

7291

1265

4621

260

2150

4621

203

196

198

393

3158

9972

894

6012

184

2452

6012

202

188

200

357

4216

17778

601

5602

124

2367

5602

201

199

193

246

2617

6849

548

6957

113

2638

6957

200

195

197

174

-1124

1263

1816

-1348

1816

199

194

181

199

-2404

5779

168

5439

-2332

5439

198

191

189

118

2022

4090

212

7726

2780

7726

197

192

162

194

2037

4150

124

5063

2250

5063

196

186

187

158

2103

4424

160

6974

2641

6974

195

177

182

122

-1766

3119

5847

-2418

5847

As shown in Table 135 the greatest distance (dst) 472. between the center of the cloud and the center of the class-205 , it is followed by: class-203 (393.), class-204 (392.), class-202 (357.), class-201 (246.), class-199 (199.), class-197 (194.), class-200 (174.), class-196 (158.), class-195 (122.), class-198 (118.).

Table 136 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 2

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

205

204

202

210

472

2310

5334

1122

2380

548

1543

3165

204

201

203

174

392

-1334

1779

309

1128

151

-1062

5749

203

196

198

393

1057

1117

100

674

821

6686

202

188

200

357

-1601

2562

807

-899

6410

201

199

193

246

-599

359

365

-604

7322

200

195

197

174

1192

1421

2044

1430

3859

199

194

181

199

-956

915

861

-928

6300

198

191

189

118

-246

114

-338

7840

197

192

162

194

898

806

983

992

6046

196

186

187

158

-478

228

360

-600

7334

195

177

182

122

-623

388

727

-853

6575

Table 137 Position of branches (dipoles) as a consequence of the center of classes in relation to the factors axis 3

knot

higher

lower

Q(n)

ind

dsd2

prd

prd2

acod

cod

ctd

cosd

+cosd2

205

204

202

210

472

189

126

3181

204

201

203

174

392

-270

-215

5795

203

196

198

393

336

113

261

6754

202

188

200

357

493

243

277

6486

201

199

193

246

106

107

7334

200

195

197

174

-212

-254

3924

199

194

181

199

1743

3039

2860

1691

9160

198

191

189

118

112

7853

197

192

162

194

-460

212

259

-509

6305

196

186

187

158

519

270

425

652

7758

195

177

182

122

697

486

911

954

7486

Table 138 Relative mutual contributions of factors (from 1 to 3) per classes

kls

knot1

knot2

Q(n)

inr

+inr

205

204

202

210

204

201

203

174

105

203

196

198

202

188

200

201

199

193

200

195

197

199

194

181

198

191

189

197

192

162

101

196

186

187

103

195

177

182

104

* Inertia is 39. For the class-205 this means that it stands out most prominently, it is followed by: class-204 (23.), class-203 (12.), class-202 (9.), class-201 (7.), class-200 (4.), class-199 (3.), class-198 (2.), class-197 (2.), class-196 (2.), class-195 (1.).

*The highest contribution of the factor to the class-205 (94.) has the 1st- factor, this means that mentioned structure have examinees of the observed class. The same can be said, with less contribution, for characteristics: factor-2 (31.), factor-3 (1.). The contribution to the class-204 (105.) belongs to 1.- factor and factor-2 (26.), factor-3 (1.). The contribution to the class-203 (74.) belongs to 1.- factor and factor-2 (8.), factor-3 (1.). The contribution to the class-202 (50.) belongs to 1.- factor and factor-2 (7.), factor-3 (1.). The contribution to the class-201 (46.) belongs to 1.- factor and factor-2 (2.), factor-3 (0.). The contribution to the class-200 (8.) belongs to 1.- factor and factor-2 (7.), factor-3 (0.). The contribution to the class-199 (14.) belongs to 1.- factor and factor-2 (7.), factor-3 (2.). The contribution to the class-198 (18.) belongs to 1.- factor and factor-2 (0.), factor-3 (0.). The contribution to the class-197 (10.) belongs to 1.- factor and factor-2 (2.), factor-3 (1.). The contribution to the class-196 (13.) belongs to 1.- factor and factor-2 (1.), factor-3 (1.). The contribution to the class-195 (8.) belongs to 1.- factor and factor-2 (1.), factor-3 (1.).

Presentation of isolated classes

Significance of dipole association coefficient (class) Q(n) is the highest for the class-203 (90.) followed by: class-201 (80.), class-202 (34.).

* Inertia is 12 for the class-203 this means that it stands out most prominently, it is followed by: class-202 (9.), class-201 (7.).

*, factor-3 (1.), factor-3 (1.), factor-3 (1.), factor-3 (1.), factor-3 (0.), factor-3 (0.), factor-2 (7.), factor-3 (0.), factor-3 (1.), factor-3 (1.), factor-3 (1.).

Structure of 3 isolated factors for anthropometric and linear hepatic measurements

Table 139 The correlation matrix

hgt

wgt

BMI

D-il

ApBo

TvBo

MxAp

MxCo

MxCr

MxCc

Comx

Vcal

hgt

1000

wgt

407

1000

BMI

-243

784

1000

D-il

102

461

411

1000

ApBo

163

564

494

471

1000

TvBo

194

628

548

342

597

1000

MxAp

205

515

403

384

472

396

1000

MxCo

107

158

-16

1000

MxCr

140

274

191

307

244

203

101

251

1000

MxCc

159

392

302

391

318

289

226

916

1000

Comx

151

226

155

122

335

301

192

719

267

324

1000

Vcal

204

443

334

369

387

380

507

665

726

731

610

1000

We found the strongest correlations (916) between Max CC (MxCc) and Maximal Crainocaudal (MxCr) . The strongest negative correlation is -243 between BMI (BMI) and height (hgt).

Table 140 The characteristic square of a factor and the percentage contribution

sqare

sum

4.867

40.556

2.046

17.051

57.607

1.316

10.964

68.571

1.174

9.782

78.353

.724

6.030

84.383

.625

5.212

89.596

.548

4.570

94.165

.373

3.107

97.272

.248

2.068

99.340

.070

.581

99.921

.007

.057

99.978

.003

.022

100.000

Table 141 Structure of 3 isolated factors for anthropometric and linear hepatic measurements

1 -factor

2 -factor

3 -factor

qlt

wrig

inr

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

hgt

142

283

-80

236

wgt

788

779

606

125

416

173

BMI

648

638

407

489

239

117

-41

D-il

486

597

356

272

-237

ApBo

621

696

484

100

344

118

134

TvBo

631

683

466

325

106

243

MxAp

495

595

354

348

121

142

MxCo

842

404

163

-682

465

227

462

214

163

MxCr

943

634

402

-444

197

-586

343

261

MxCc

930

724

524

108

-338

114

-540

292

222

Comx

798

557

310

-491

241

118

497

247

188

Vcal

905

845

713

147

-437

191

-18

12.0

1000

The isolated factors structure anthropometric and linear hepatic measurements

* Decreased communality shows that the structure of 3 isolated factors does not contain enough information about 1 anthropometric and linear hepatic measurement: height (hgt) 142

The variables that contribute in forming the structure of each isolated factor are: Maximal Crainocaudal, Max CC, liver volume (calculated by formula), Maximal Coronal, Cormax LL, weight, BMI, Transverse body dimension, AP body dimension, Maximal Ap, Diaphragm to iliac, the variables that do not contribute to factor structure are: height.

* Structure of the 2nd- isolated factor is formed of 1 anthropometric and linear hepatic measurement: Maximal Coronal (MxCo) with factor contribution (cor) 465.

* Several factors contribute to variable for: Maximal Crainocaudal, factor-1 (403), factor-3 (344), Max CC, factor-1 (525), factor-3 (292).

Concordance of anthropometric and linear hepatic measurements and the structure of isolated factors

1. – for 36 (34.95%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 1 isolated factor. Latently related to the structure are 17 (16.50%) examinees. For 23 examinees we found direct proportionality, and 30 examinees were inversely related.

2. – for 15 (14.56%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 2 isolated factor. Latently related to the structure are 13 (12.62%). For 14 we found direct proportionality, and 14 were inversely related.

3. – for 6 (5.83%) examinees anthropometric and linear hepatic measurements are highly concordant with the structure 3 isolated factor. Latently related to the structure are 5 (4.85%). For 7 we found direct proportionality, and 4 were inversely related.

Concordance anthropometric and linear hepatic measurements with the structure: one factor have 57 examinees , latent agreement only have 24 examinees, with no agreement are 22 examinees.

It should be noted that 5 examinees stands out from the rest (inr)

Graph 45 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure

Graph 46 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 2F

Graph 47 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 1F and 3F

Graph 48 Representation of the anthropometric and linear hepatic measurements in the isolated factors structure 2F and 3F

Table 142 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-0,::GrpD-0

.10

::GrpD-0,::GrpD-0

.13

::GrpD-0,::GrpD-0

.15

::GrpD-2,::GrpD-0

.19

::GrpD-0,::GrpD-0

.25

::GrpD-2,::GrpD-3

.27

::GrpD-2,::GrpD-0

.47

::GrpD-0,::GrpD-0

.69

::GrpD-1,::GrpD-0

.71

::GrpD-1,::GrpD-0

1.55

::GrpD-1,::GrpD-2

2.35

From the dendrogram shown we found that the closest were groups ::GrpD-0 and:GrpD-0 with the distance.10.The biggest difference is between::GrpD-1 and:GrpD-2, with the distance 2.35.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3) ;;GrpD-0;; (4) ;;GrpD-0;; (5) ;;GrpD-0;; (6) ;;GrpD-0;; (7) ;;GrpD-0;; (8) ;;GrpD-0;; (9) ;;GrpD-0;; (10) ;;GrpD-0;; (11) ;;GrpD-0;; (12)

The mutual contribution of the division classes and factors structure for anthropometric and linear hepatic measurements

Table 143 Mutual contributions among division groups (3) and isolated factors structure

1-factor

2-factor

3-factor

mass

inr

kvl

krd

cor

ctr

krd

cor

ctr

krd

cor

ctr

::GrpD-1

320

1000

1862

997

228

-27

-89

::GrpD-2

301

1000

-927

247

-1614

748

383

-132

::GrpD-3

379

1000

-838

288

1306

699

316

181

As shown in Table 143 we found that the highest weight was 379. for class ;;GrpD-3;; This means that the biggest part of the sample which belongs to one class, belongs to this class which corresponds to the specified weighting factor, and the next is for the class: ;;GrpD-1;; (320.), ;;GrpD-2;; (301.).

* Inertia (inr) of the class ;;GrpD-1;; is 93it means that this class stands out from the rest, and the next is for class: ;;GrpD-2;; (87.), ;;GrpD-3;; (77.).

* Relative contribution of the class ;;GrpD-1;; to inertia of the 1st – axis is228., then for: ;;GrpD-3;; (55.), ;;GrpD-2;; (53.). Relative contribution of the class ;;GrpD-2;; to inertia of the 2nd – axis is383, then for: ;;GrpD-3;; (316.), ;;GrpD-1;; (0.). Relative contribution of the class ;;GrpD-3;; inertia 3. – axis is9, then for: ;;GrpD-2;; (4.), ;;GrpD-1;; (2.).

* Association of the classes on the 1st – axis is inversely proportional for class ;;GrpD-3;;, ;;GrpD-2;;, and inversely proportional for the class, ;;GrpD-2;;, ;;GrpD-1;;, and inversely proportional for the class, ;;GrpD-2;;, ;;GrpD-1;;.

Table 144 Contribution of each factor to a class in ‰:

::GrpD-1

997

::GrpD-2

247

748

::GrpD-3

288

699

* The factor F1 gives the highest contribution to the class ::GrpD-1 (997 :‰:) then F3 (2‰) which 498.5 times contribute less.

Table 145 Mahalanobis distance between ;;GrpD;; in relation to anthropometric and linear hepatic measurements

::GrpD-1

::GrpD-2

::GrpD-3

::GrpD-1

.00

2.55

2.30

::GrpD-2

2.55

.00

3.78

::GrpD-3

2.30

3.78

.00

By calculating the Mahalanobis distance between ;; GrpD ;; we obtained another indicator of similarities or differences. Distances of different spaces can be compared. According to results in the table we can say that the distance is minimal between ;;GrpD;;: ;;GrpD-3;; and ;;GrpD-1;; (::GrpD-3 and:GrpD-1 (2.30) (bigger). The farthest are;;GrpD;; : ;;GrpD-3;; and ;;GrpD-2;; (::GrpD-3 and:GrpD-2 (3.78) (bigger).

Table 146 Grouping ;;GrpD;; in relation to anthropometric and linear hepatic measurements

level

closeness

::GrpD-1,::GrpD-3

2.30

::GrpD-1,::GrpD-2

3.23

From the dendrogram shown we found that the closest were groups ::GrpD-1 and:GrpD-3 with the distance2.30.The biggest difference is between::GrpD-1 and:GrpD-2, distance 3.23.

Legend: ;;GrpD-1;; (1) ;;GrpD-2;; (2) ;;GrpD-3;; (3)

The post Sample of 152 SAMPLE OF 152 Basic parameters of observed anthropometric characteristics appeared first on essayfab.

Sample of 152 SAMPLE OF 152 Basic parameters of observed anthropometric characteristics

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