Possible Causes of Three-Dimensional Structural Deviations in the Neighborhood of Cranial Landmarks: Occlusal Force and Aging

Possible Causes of Three-Dimensional Structural Deviations in the Neighborhood of Cranial Landmarks: Occlusal Force and Aging

Yuji Mizoguchi

Department of Anthropology, National Museum of Nature and Science 4–1–1 Amakubo, Tsukuba, Ibaraki 305–0005, Japan

E-mail: [email protected]

Abstract To seek the causes of three-dimensional morphological variations in the human skull, correlations between the 3D structural deviations in the neighborhood of cranial landmarks obtained by the finite element scaling method and the degree of dental wear or age were examined by principal component analysis using three male adult samples from Japanese, Indians, and Afri- can-Americans. The results showed that the degree of dental wear is positively associated with the magnitude of strain at the inion in Japanese; that dental wear is inversely associated with the mag- nitude of strain at the frontotemporale in Japanese; and that age is positively associated with the magnitude of strain at the center of the parietal tuber in African-Americans. These significant asso- ciations suggest, at least, that the craniofacial form varies along with age even in adulthood and, possibly, also in response to mechanical stresses from the masticatory and/or nuchal muscles.

Key words : Human cranial form, Three-dimensional coordinates, Finite element scaling analysis, Dental wear, Age

In recent years, with the development of appa- ratus and software for capturing and analyzing three-dimensional (3D) coordinates, many geo- metric morphometric (Marcus et al., 1996) stud- ies have been carried out in the field of physical anthropology. Although most of them were based on the generalized Procrustes analysis (e.g., Detroit, 2000; Bookstein, 1991; Hennessy and Stringer, 2002; Bookstein

2003; Slice, 2005; Gunz and Harvati, 2007; Gunz

Ogihara, 2009; Bigoni

and Kondo, 2010; Harvati et al., 2010; Neubauer

badel, 2011; Weisensee and Jantz, 2011; Frei- dline

mon-Taubadel and Smith, 2012), there is another useful method to quantify the magnitude and direction of strain at an arbitrary point of a 3D form in the change from the form to another cor- responding form. This method is the

ment scaling method (FESM). This was devel- oped by Lewis

(1983), and their colleagues in the 1980s and has been used by several researchers (Cheverud and Richtsmeier, 1986; Richtsmeier, 1987; Mine and Ogata, 1989; Cheverud et al., 1992; Kohn et al., 1993, 1995; Richtsmeier and Walker, 1993;

Mizoguchi, 2000a, b, 2005; Matsukawa, 2002).

Both methods are useful for the analysis of form and have many similar strong points. However, one of the major differences between them is that, in generalized Procrustes analysis (GPA), original configurations are standardized by the centroid size, while in

analysis (FESA), size is not removed.

In the present study, using the FESM, it is

examined whether or not there are any associa-

tions between 3D structural deviations in the

neighborhood of some cranial landmarks and the

degree of occlusal wear on the maxillary

molar (UM1) or age, in order to explore the pos-

sibility that masticatory force and/or aging are

causes of part of the morphological variation in

the human skull.

Materials and Methods

Three male adult samples were used. One con- sists of 37 skulls of Japanese from the end of the early modern “Edo” period (A.D. 1603 to 1867).

These are stored in the University Museum, the University of Tokyo, Japan. The second sample is composed of 30 skulls of African-Americans randomly extracted from the Terry Collection housed in the National Museum of Natural His- tory, Smithsonian Institution, Washington, D.C., U.S.A. They died during the period of 1926 to 1944, and the age-at-death ranges from 21 to 68.

The

which are stored in Nihon University School of Dentistry at Matsudo, Chiba, Japan.

Age-at-death is known for individual speci- mens of the Terry Collection. For the other two samples, however, there are no such records.

Therefore, the degree of occlusal wear on the UM1 was recorded as an indicator of age accord- ing to Brocaʼs grading system (Martin and Saller, 1957). It is to be regretted, however, that the present author did not record the degree of dental wear for the sample from the Terry Collection because he did not intend to analyze the relation- ship between occlusal force and age at that time.

Erasing the effect of aging from dental wear is a future task.

All 3D coordinates for cranial landmarks were obtained by the present author on the basis of trigonometric measurements using sliding and spreading calipers. The Japanese skulls were measured twice to assess intra-observer errors during the periods of September, 1976, to Janu- ary, 1977, and September, 1977, to December, 1977; the African-American skulls, in April and May, 1987; and the Indian skulls, between April, 1994, and October, 1996. Basically, the coordi- nates of a landmark are calculated using the line segments between the landmark and three of the following

lambda, right asterion, and left asterion. In the

or anterior-posterior axis of the skull points to the anterior side; that of the y-axis or medial-lat- eral axis points to the left; and that of the z-axis or superior-inferior axis points to the superior.

The practical objects analyzed by FESM are six elements or hexahedra set in the cranium (Fig. 1). The eight nodes of each hexahedron are as follows.

1) Right element 1 (anterior neurocranium):

nasion (n), grabella (g), bregma (b), basion (ba), right frontotemporale (ft), the center of the right frontal tuber (STH), right eurion (eu), and right porion (po)

2) Left element 1 (anterior neurocranium): n, g, b, ba, left ft, left STH, left eu, and left po 3) Right element 2 (posterior neurocranium): b,

ba, inion (i), lambda (l), right eu, right po, right asterion (ast), and the center of the right parietal tuber (SCH)

4) Left element 2 (posterior neurocranium): b, ba, i, l, left eu, left po, left ast, and left SCH 5) Right element 3 (orbito-zygomatic region): g,

right frontomalare temporale (fmt), right po, opisthion (o), n, right orbitale (or), right zygo- maxillare (zm), and ba

6) Left element 3 (orbito-zygomatic region): g, left fmt, left po, o, n, left or, left zm, and ba The definitions of the above landmarks except for STH and SCH can be found in Martin and Saller (1957). STH was marked with a pencil by viewing from superior and lateral directions, and SCH, from superior and posterior directions.

This method may be somewhat subjective.

For each node of the six hexahedra, the magni-

tude of 3D structural deviation (from the ʻmeanʼ

cranium in each sample) called

and its direction cosines were first estimated by

FESM. The details of the FESM and the relevant

procedures are described in Lewis et al. (1980),

Cheverud

meier (1986), Leigh and Cheverud (1991),

Cheverud

and Wilson (1976), and Mizoguchi (2000b). In

ized using the following formula (Cheverud and Richtsmeier, 1986; Cheverud et al., 1992) before use in multivariate analyses:

L_i＝ln [(1＋2P_i

)

],

where P

is the

3), and L

is the value transformed to a linear or additive scale.

The intra-observer errors for linearized princi- pal values and direction cosines were evaluated

by the double determination method (Lundström, 1948; Mizoguchi, 1977). To check the relative magnitude of errors, intraclass correlation coeffi- cients (Cavalli-Sforza and Bodmer, 1971) were calculated between the duplicate data sets of the early modern Japanese sample.

To examine the overall or local relationships between 3D structural strains and dental wear or age, principal component analysis, often abbrevi- ated to PCA, (Lawley and Maxwell, 1963;

Fig. 1. Elements set up in the cranium and the cranial landmarks used. a. Birdʼs-eye view. b. Anterior view. c.

Lateral view. d. Inferior view.

Okuno

1972) was applied to the correlation matrices.

The correlations between age and the principal values and direction cosines were estimated using Pearsonʼs product-moment correlation coefficient, and those between such 3D variables and the degree of occlusal wear on the UM1 were estimated using four-fold point correlation coefficient (Yasuda, 1969).

At this step, however, only six nodes were selected for a set of three elements on one side because of the statistical limitation on the num- ber of variables and sample size. In practice, one set of six nodes was chosen from the viewpoint of a possible relationship with the degree of development of skeletal muscles or growth: ft, STH, i, SCH, g, and zm; and the other set mainly contains intersections of sutures: b, ba, l, ast, fmt, and n.

The number of principal components was determined so that the cumulative proportion of the variances of the principal components exceeded 80%. The principal components obtained were then transformed by Kaiserʼs nor- mal varimax rotation method (Asano, 1971;

Okuno

attempt to reveal other associations behind the variables.

The significance of factor loadings was tested by the bootstrap method (Efron, 1979a, b, 1982;

Diaconis and Efron, 1983; Mizoguchi, 1993). In order to estimate the bootstrap standard deviation of a factor loading, 1,000 bootstrap replications, including the observed sample, were used. The bootstrap standard deviation was estimated by directly counting the cumulative frequency for the standard deviation in the bootstrap distribution.

The presence of common factors, such as those represented by principal components (PCs) or rotated factors (Facs), was further tested by eval- uating the similarities between the factors obtained for the three samples, namely, by esti- mating Kendall's rank correlation coefficient, tau (Siegel, 1956), between the patterns of variation of factor loadings. It should be noted here that a

from the PCA for a certain sample can be detected as a rotated factor in the rotated solution of the PCs extracted from another similar sample, as shown in Mizoguchi (2004). Therefore, PCs and Facs are equivalently treated in this study.

Mathematical and statistical calculations were executed using programs written by the author in FORTRAN: THRCR3 for calculating 3D coordi- nates of cranial landmarks, FESM for

ment scaling analysis, MIVCRL for intraclass correlation coefficients, BTPCA for principal component analysis and Kaiser's normal varimax rotation, and RKCNCT for rank correlation coef-

FTN77 for personal computers, provided by Sal- ford Software Ltd. To increase efficiency during programming and calculation, a GUI for pro- gramming, CPad, provided by

3D illustrations of the human skull were drawn by the present author with Rokkaku-Daiou Super 6 (Ver. 6.3.1) of CELSYS, Inc., utilizing a free 3D model,

by Fahim Fazli as a template.

Results

Intraclass correlations between the duplicate

data sets from the early modern Japanese sample

are shown in Table 1. The intraclass correlation

coefficients independently obtained from the

right and left sides reveal at least two similar ten-

dencies. One is that the intra-observer errors on

the principal values tend to be lower than those

on the corresponding direction cosines in most of

the landmarks examined. The other is that,

against our expectation, while the intraclass cor-

relation coefficients on the nasion and glabella

are extremely low, those on the inion and SCH

are relatively high. Such a difference may be

partly caused by the use of different sets of three

landmarks on which the determination of the

coordinates of landmarks in question is based. In

any case, the results of the following analyses,

especially on the nasion and glabella, must be

carefully interpreted.

Table 1. Intraclass correlation coefficients between the first and second data sets from early modern Japanese in the linearized first principal values and their direction cosines at the eight nodes and centroid of each of six regional elements (hexahedra) of the skull.¹

Variable² Right Left Variable² Right Left

Element 1 (Anterior neurocranium) Element 2 (Posterior neurocranium)

Node 1 (n): 1st p.v. 0.17 0.23 Node 6 (po): 1st p.v. 0.85*** 0.81***

a–p 0.40** 0.64*** a–p 0.65*** 0.58***

m–l 0.05 0.13 m–l 0.83*** 0.51***

s–i 0.68*** 0.32* s–i 0.70*** 0.59***

Node 2 (g): 1st p.v. 0.17 0.20 Node 7 (ast): 1st p.v. 0.83*** 0.63***

a–p 0.47** 0.35* a–p 0.86*** 0.52***

m–l −0.10³ 0.56*** m–l 0.54*** 0.62***

s–i 0.37* 0.40** s–i 0.70*** 0.71***

Node 3 (b): 1st p.v. 0.91*** 0.90*** Node 8 (SCH): 1st p.v. 0.85*** 0.89***

a–p 0.28* 0.66*** a–p 0.54*** 0.76***

m–l 0.41** 0.28* m–l 0.42** 0.53***

s–i 0.52*** 0.68*** s–i 0.45** 0.50***

Node 4 (ba): 1st p.v. 0.75*** 0.78*** Centroid: 1st p.v. 0.87*** 0.90***

a–p 0.72*** 0.84*** a–p 0.85*** 0.68***

m–l 0.71*** 0.39** m–l 0.86*** 0.47**

s–i 0.68*** 0.71*** s-i 0.85*** 0.68***

Node 5 (ft): 1st p.v. 0.80*** 0.82*** Element 3 (Orbito-zygomatic region)

a–p 0.43** 0.61*** Node 1 (g): 1st p.v. 0.25 0.26

m–l 0.43** 0.57*** a–p 0.43** 0.51***

s–i 0.62*** 0.50*** m–l 0.34* 0.00

Node 6 (STH): 1st p.v. 0.55*** 0.63*** s–i 0.68*** 0.44**

a–p 0.43** 0.34* Node 2 (fmt): 1st p.v. 0.59*** 0.46**

m–l 0.45** 0.28* a–p 0.22 0.51***

s–i 0.07 0.46** m–l 0.37* 0.58***

Node 7 (eu): 1st p.v. 0.91*** 0.89*** s–i 0.53*** 0.53***

a–p 0.73*** 0.47** Node 3 (po): 1st p.v. 0.76*** 0.76***

m–l 0.55*** 0.36* a–p 0.72*** 0.60***

s–i 0.61*** 0.56*** m–l 0.70*** 0.19

Node 8 (po): 1st p.v. 0.88*** 0.86*** s–i 0.75*** 0.27

a–p 0.53*** 0.90*** Node 4 (o): 1st p.v. 0.79*** 0.84***

m–l 0.64*** 0.83*** a–p 0.61*** 0.43**

s–i 0.41** 0.85*** m–l 0.19 0.23

Centroid: 1st p.v. 0.95*** 0.94*** s–i 0.68*** 0.58***

a–p 0.66*** 0.51*** Node 5 (n): 1st p.v. 0.30* 0.09

m–l 0.68*** 0.37* a–p 0.64*** 0.14

s–i 0.71*** 0.63*** m–l 0.34* 0.02

Element 2 (Posterior neurocranium) s–i 0.55*** 0.47**

Node 1 (b): 1st p.v. 0.95*** 0.93*** Node 6 (or): 1st p.v. 0.66*** 0.74***

a–p 0.71*** 0.73*** a–p 0.78*** 0.42**

m–l 0.68*** 0.36* m–l 0.66*** 0.43**

s–i 0.62*** 0.41** s–i 0.55*** 0.21

Node 2 (ba): 1st p.v. 0.68*** 0.85*** Node 7 (zm): 1st p.v. 0.79*** 0.76***

a–p 0.68*** 0.37* a–p 0.31* 0.45**

m–l 0.43** 0.39** m–l 0.40** 0.62***

s–i 0.60*** 0.71*** s–i 0.72*** 0.49**

Node 3 (i): 1st p.v. 0.97*** 0.92*** Node 8 (ba): 1st p.v. 0.82*** 0.69***

a–p 0.89*** 0.60*** a–p 0.45** 0.57***

m–l 0.81*** 0.67*** m–l 0.47** 0.56***

s–i 0.97*** 0.92*** s–i 0.42** 0.70***

Node 4 (l): 1st p.v. 0.95*** 0.96*** Centroid: 1st p.v. 0.67*** 0.80***

a–p 0.75*** 0.74*** a–p 0.81*** 0.75***

m–l 0.86*** 0.61*** m–l 0.68*** 0.46**

s–i 0.73*** 0.55*** s–i 0.75*** 0.57***

Node 5 (eu): 1st p.v. 0.65*** 0.80***

a–p 0.58*** 0.79***

m–l 0.33* 0.36*

s–i 0.36* 0.59***

1 The sample size (i.e., no. of pairs) is 32.

2 p.v.: principal value; a–p: direction cosine for the anterior-posterior axis; m–l: direction cosine for the medial-lateral axis;

s–i: direction cosine for the superior-inferior axis.

3 Underestimate due to a sampling error.

* P＜0.05; ** P＜0.01; *** P＜0.001, by a one-tailed test.

and rotated factors for ft, STH, i, SCH, g, and zm are listed, and, in Tables 14 to 25, those for b, ba, l, ast, fmt, and n are shown. Remarkable findings are as follows.

First, both PC IV from the right elements (Table 2) and PC VIII from the left elements (Table 4) of early modern Japanese have highly significant correlations (P＜0.001) with the degree of dental wear and the first principal value at the inion (Fig. 2). Furthermore, both PC VIIIs from the right and left elements (Tables 2 and 4) have highly significant positive correlations (P＜0.001) with dental wear and inverse correla- tions (P＜0.01) with the

the frontotemporale.

Not only Fac II from the right elements (Table 11) but also Fac IX from the left elements (Table 13) of African-Americans reveals that age is sig- nificantly associated with the principal value at SCH (P＜0.01). This association is confirmed by the significant rank correlation coefficient of 0.53 (P＜0.001) between these factors in the pattern of variation of factor loadings (Table 26).

Both PC IV from the right elements (Table 14) and PC VIII from the left elements (Table 16) of early modern Japanese show that the degree of dental wear is positively associated with the prin- cipal value at the frontomalare temporale (P＜0.01) and inversely associated with the prin- cipal value at the asterion (P＜0.001).

In the data set of Indians, however, no consis- tent tendency was found with respect to the asso- ciations between dental wear and 3D structural deviations at landmarks.

Discussion

To date, several FESAs of the human skull have been conducted. For example, Cheverud et

ined the effect of artificial cranial vault deforma- tion on the cranial base and face using Native American samples; Richtsmeier (1987) studied morphological differences between the craniofa- cial complex of normal individuals and those

zon; and Richtsmeier and Walker (1993) extracted properties of the facial skeleton of a juvenile

from Nariokotome, Kenya, by comparison with the faces of some modern humans, chimpanzees, and simulated

present authorʼs knowledge, however, there have been no FESAs on the associations of cranial landmarks with dental wear, except for those by Mizoguchi (2000a, 2005).

Associations with dental wear or age

Mizoguchi (2000a), using the same sample from early modern Japanese as used here, carried out FESAs of three neurocranial elements, which were however different from those examined in the present study, and showed that the local shape differences (the so-called standard devia- tion of transformed principal value) at left fron- tomalare temporale and left orbitale were inversely correlated with the degree of occlusal wear on the UM1. This implies that those indi- viduals who have weaker dental wear tend to have a more distorted face in the regions near the temporalis muscle.

Furthermore, Mizoguchi (2005), using the same sample and the same neurocranial elements as in his previous work (2000a), revealed that the neurocranium of a person having heavily worn molars tended to be

anterior-superior part (left STH and right and left ft) and narrower and higher in its posterior-infe- rior part (right ast and right and left po). He con- sidered that this result suggests that the neurocra- nial form may partly be determined or modified by the development of the masticatory muscles that produce dental wear. It should be noted in his analyses, however, that, while dental wear was associated with the direction of 3D devia- tions, it was not so strongly related with their magnitude.

In the present study, a different set of elements

from that used by Mizoguchi (2000a, 2005) was

examined. Although Mizoguchi (2000a, 2005)

dealt with only a limited part of the face, the

Table 2.Principal component analysis of the correlations between the linearizedfirst principal values and their direction cosines at six craniofacial landmarks, i.e., ft, STH, i, SCH, g, and zm in the three right elements, and the degree of occlusal wear on the maxillary first molar in early modern Japanese.1 Variable2Factor loadingsTotal variance (%)PC IIIIIIIVVVIVIIVIIIIXXXI Node 5 (ft) of Element 1: 1st p.v.0.100.48***0.50***−0.010.32***0.020.26***−0.15***0.040.15***0.25***77.25 a–p−0.54***−0.000.03−0.550.30−0.16−0.32−0.19−0.01−0.10−0.1087.79 m–l−0.03−0.040.060.34−0.33−0.390.57*0.200.28−0.200.1187.94 s–i0.55***−0.08−0.560.29−0.080.300.110.01−0.180.130.1487.80 Node 6 (STH) of Element 1: 1st p.v.0.64**0.010.39***0.27***0.21***−0.22***−0.040.18***−0.040.17***0.20***83.14 a–p0.56***−0.51−0.35−0.010.03−0.03−0.18−0.050.04−0.16−0.1377.10 m–l−0.56***0.16−0.260.210.09−0.370.090.43*−0.250.020.0385.23 s–i−0.060.440.24−0.22−0.210.430.44−0.060.180.23−0.29*90.02 Node 3 (i) of Element 2: 1st p.v.−0.46*−0.46***0.19**−0.21***0.13**0.14***0.19***−0.20***0.29***0.18***0.12***74.22 a–p0.63***−0.02−0.03−0.180.390.350.270.07−0.12−0.22−0.0484.65 m–l0.100.340.060.460.15−0.22−0.47−0.160.230.240.0076.14 s–i−0.64***−0.25−0.13−0.20−0.360.05−0.08−0.050.190.070.40***88.07 Node 8 (SCH) of Element 2: 1st p.v.0.19−0.130.030.030.69***−0.48**0.18−0.160.10−0.05−0.0483.34 a–p−0.62***0.35−0.400.400.100.170.110.05−0.010.07−0.0188.57 m–l−0.28−0.10−0.170.57*0.240.30−0.230.020.240.070.1171.87 s–i0.52***−0.330.45−0.18−0.28−0.280.020.040.050.080.1981.84 Node 1 (g) of Element 3: 1st p.v.−0.330.64***0.09−0.15−0.11−0.22**−0.15*0.04−0.07−0.33***−0.0174.66 a–p−0.08−0.82***−0.130.130.00−0.080.02−0.170.000.08−0.1277.93 m–l−0.06−0.050.510.120.250.21−0.230.48*0.32−0.00−0.28*85.88 s–i0.38*0.62−0.30−0.140.11−0.06−0.05−0.32*−0.070.200.1481.45 Node 7 (zm) of Element 3: 1st p.v.−0.22−0.14***0.38***0.19***0.32***0.49***−0.07−0.02−0.15***−0.42***0.37***93.41 a–p0.33*0.31−0.48−0.310.03−0.02−0.050.070.50**−0.260.24*92.08 m–l−0.62***−0.230.09−0.020.35−0.150.27−0.08−0.240.120.0774.32 s–i0.070.070.560.28−0.520.03−0.26−0.21−0.20−0.090.0384.35 Occlusal wear of UM10.09−0.08−0.07−0.57***0.070.10−0.210.53***−0.140.34*0.2185.66 Total contribution (%)17.03 12.09 9.958.467.776.545.794.513.893.593.3682.99 Cumulative proportion (%)17.03 29.12 39.07 47.53 55.30 61.85 67.64 72.15 76.04 79.63 82.99 82.99 1 The sample size is 33. The number of principal components shown here was determined so that the cumulative proportion of the variances of the principal components exceeded 80%. 2 p.v.: principal value; a–p: direction cosine for the anterior-posterior axis; m–l: direction cosine for the medial-lateral axis; s–i: direction cosine for the superior-inferior axis.

* P＜0.05; *

* **P＜0.01; * P＜0.001, by a two-tailed bootstrap test.

ble 3.Rotated solution of thefirst eleven principal components extracted from the correlations between the linearizedfirst principal values and their direction cosines at six craniofacial landmarks, i.e., ft, STH, i, SCH, g, and zm in the three right elements, and the degree of occlusal wear on the maxillary first molar in early modern Japanese.1 Variable2Factor loadings Fac IIIIIIIVVVIVIIVIIIIXXXI e 5 (ft) of Element 1: 1st p.v.0.150.020.78**0.010.250.21−0.15−0.02−0.04−0.05−0.06 a–p−0.130.01−0.09−0.42*0.18−0.000.080.11−0.00−0.72***0.33* m–l0.04−0.010.030.90***0.03−0.100.07−0.200.030.050.04 s–i−0.100.32−0.19−0.04−0.08−0.000.020.060.180.78***−0.28 e 6 (STH) of Element 1: 1st p.v.0.51*−0.130.160.150.290.14−0.370.16−0.100.31−0.37 a–p0.300.03−0.63*−0.160.17−0.070.07−0.080.230.37**−0.12 m–l−0.60*0.06−0.110.42*0.10−0.06−0.050.34*−0.26−0.30*−0.10 s–i−0.08−0.190.73***−0.09−0.28−0.300.33*−0.190.050.080.07 e 3 (i) of Element 2: 1st p.v.0.01−0.130.04−0.050.120.080.13−0.03−0.14−0.040.82*** a–p0.21−0.070.13−0.240.350.240.43*

0.010.250.43**−0.34 m–l−0.07−0.070.08−0.090.07−0.09−0.82***−0.140.05−0.03−0.19 s–i−0.170.18−0.150.15−0.400.08−0.010.190.05−0.240.71*** e 8 (SCH) of Element 2: 1st p.v.0.110.01−0.040.040.89***0.00−0.11−0.10−0.00−0.04−0.02 a–p−0.90***0.070.130.13−0.100.03−0.14−0.05−0.06−0.020.06 m–l−0.49**−0.24−0.15−0.02−0.030.29−0.43−0.110.020.270.21 s–i0.86***−0.01−0.040.20−0.02−0.05−0.020.11−0.050.100.03 e 1 (g) of Element 3: 1st p.v.−0.200.100.240.09−0.170.03−0.03−0.030.13−0.70***−0.29 a–p0.10−0.02−0.60−0.000.15−0.060.06−0.14−0.300.260.44** m–l0.05−0.89***0.10−0.040.020.13−0.130.09−0.06−0.07−0.03 s–i−0.020.50*0.37−0.280.11−0.20−0.220.020.35*0.07−0.34* e 7 (zm) of Element 3: 1st p.v.−0.07−0.180.08−0.11−0.030.92***0.07−0.08−0.12−0.010.12 a–p−0.010.13−0.000.040.09−0.080.010.100.93***−0.01−0.09 m–l−0.310.090.040.070.340.140.130.10−0.50**−0.220.41** s–i0.41**0.000.090.06−0.55**0.19−0.25−0.31−0.35*−0.13−0.18 lusal wear of UM10.15−0.09−0.00−0.23−0.06−0.080.150.85***0.100.000.04 The sample size is 33. The cumulative proportion of the variances of the eleven principal components is 82.99%. p.v.: principal value; a–p: direction cosine for the anterior-posterior axis; m–l: direction cosine for the medial-lateral axis; s–i: direction cosine for the superior-inferior axis.

* P＜0.05; *

* **P＜0.01; *P＜0.001, by a two-tailed bootstrap test.

Table 4.Principal component analysis of the correlations between the linearizedfirst principal values and their direction cosines at six craniofacial landmarks, i.e., ft, STH, i, SCH, g, and zm in the three left elements, and the degree of occlusal wear on the maxillary first molar in early modern Japanese.1 Variable2Factor loadingsTotal variance (%)PC IIIIIIIVVVIVIIVIIIIXX Node 5 (ft) of Element 1: 1st p.v.−0.320.150.56***−0.36***0.42***0.14*0.08−0.18**0.090.0681.59 a–p0.56***−0.050.53−0.05−0.08−0.340.110.270.30*−0.0390.26 m–l0.67***−0.02−0.45−0.14−0.030.23−0.23−0.120.180.1283.69 s–i−0.61***−0.06−0.070.29−0.18−0.080.09−0.00−0.290.38*73.71 Node 6 (STH) of Element 1: 1st p.v.−0.180.62***0.21*−0.140.48***0.16*0.39***−0.01−0.15−0.0791.31 a–p0.43**0.15−0.08−0.07−0.00−0.230.52*0.48*−0.07−0.1178.61 m–l0.73***−0.11−0.26−0.140.100.12−0.29−0.18−0.050.2081.78 s–i−0.61***−0.150.260.34−0.260.01−0.14−0.000.220.2979.47 Node 3 (i) of Element 2: 1st p.v.0.24−0.30***0.27***0.59***0.26***0.18***−0.11**0.16***−0.02−0.18***73.71 a–p0.020.27−0.11−0.09−0.470.350.58**0.050.120.1180.39 m–l−0.51***−0.04−0.07−0.040.31−0.26−0.340.46*−0.12−0.0478.49 s–i0.29−0.490.420.48−0.30−0.07−0.09−0.200.05−0.0486.15 Node 8 (SCH) of Element 2: 1st p.v.0.150.54***0.39*0.290.050.25−0.33**0.31**0.00−0.1083.57 a–p−0.29*−0.260.02−0.09−0.060.80***0.040.130.26−0.0489.25 m–l−0.29−0.45−0.51−0.19−0.12−0.440.110.01−0.01−0.0580.61 s–i0.38**0.320.46−0.030.05−0.39*0.07−0.20−0.240.44**91.66 Node 1 (g) of Element 3: 1st p.v.−0.06−0.31***0.43***−0.50***0.00−0.02−0.25**0.15−0.21**−0.0567.07 a–p0.07−0.03−0.150.68*0.23−0.090.41−0.31−0.03−0.1985.42 m–l0.000.40−0.28−0.120.40−0.09−0.100.040.52**0.34*82.32 s–i0.17−0.130.34−0.42−0.570.210.080.13−0.26*0.0880.49 Node 7 (zm) of Element 3: 1st p.v.0.040.61***0.100.50***−0.27***−0.01−0.13*0.10*0.050.15***76.49 a–p−0.01−0.61**0.40−0.180.22−0.180.21−0.150.38*0.0184.80 m–l0.31−0.33−0.180.110.390.320.020.15−0.51**0.1982.27 s–i−0.060.64**−0.13−0.16−0.38−0.22−0.29−0.100.02−0.34*85.68 Occlusal wear of UM10.10−0.23−0.180.17−0.01−0.070.100.71***0.180.1970.47 Total contribution (%)12.99 12.44 10.16 9.517.917.296.426.065.113.7081.57 Cumulative proportion (%)12.99 25.42 35.59 45.10 53.01 60.29 66.71 72.77 77.87 81.57 81.57 1 The sample size is 33. The number of principal components shown here was determined so that the cumulative proportion of the variances of the principal components exceeded 80%. 2 p.v.: principal value; a–p: direction cosine for the anterior-posterior axis; m–l: direction cosine for the medial-lateral axis; s–i: direction cosine for the superior-inferior axis. * P＜0.05; ** P＜0.01; ***P＜0.001, by a two-tailed bootstrap test.

ble 5.Rotated solution of the first ten principal components extracted from the correlations between the linearizedfirst principal values and their direction cosines at six craniofacial landmarks, i.e., ft, STH, i, SCH, g, and zm in the three left elements, and the degree of occlusal wear on the maxillary first molar in early modern Japanese.1 Variable2Factor loadings Fac IIIIIIIVVVIVIIVIIIIXX e 5 (ft) of Element 1: 1st p.v.−0.15−0.010.12−0.250.67*−0.01−0.05−0.310.380.13 a–p0.230.170.28−0.16−0.12−0.350.050.460.60**−0.06 m–l0.72***−0.140.01−0.01−0.39*0.040.20−0.05−0.130.30* s–i−0.76*−0.17−0.170.06−0.06−0.070.03−0.11−0.28−0.02 e 6 (STH) of Element 1: 1st p.v.−0.03−0.000.220.120.90***−0.090.080.03−0.130.10 a–p0.24−0.00−0.040.070.16−0.200.170.78***−0.03−0.09 m–l0.71***−0.310.02−0.08−0.34*−0.200.06−0.14−0.060.17 s–i−0.78**0.070.12−0.03−0.250.15−0.00−0.220.160.10 e 3 (i) of Element 2: 1st p.v.0.03−0.360.450.33−0.190.14−0.260.080.29−0.28 a–p−0.090.12−0.01−0.010.120.170.81***0.22−0.170.01 m–l−0.350.00−0.09−0.180.110.13−0.71***0.17−0.180.14 s–i−0.08−0.100.220.15−0.55*−0.140.07−0.130.49**−0.44* e 8 (SCH) of Element 2: 1st p.v.0.030.100.88***−0.060.10−0.00−0.130.08−0.140.00 a–p−0.12−0.220.12−0.200.060.82***0.27−0.150.120.04 m–l−0.140.10−0.81***0.03−0.230.07−0.190.15−0.060.00 s–i0.03−0.070.23−0.110.13−0.89***0.13−0.040.130.04 e 1 (g) of Element 3: 1st p.v.0.02−0.07−0.06−0.67*0.10−0.02−0.26−0.060.24−0.26 a–p−0.05−0.14−0.010.89***0.02−0.080.060.000.07−0.19 m–l0.130.100.050.110.15−0.03−0.080.04−0.010.87*** s–i0.02−0.010.02−0.67**−0.08−0.060.44*0.070.02−0.39* e 7 (zm) of Element 3: 1st p.v.−0.240.240.62*0.21−0.15−0.220.150.07−0.320.13 a–p−0.04−0.09−0.28−0.060.030.03−0.06−0.040.86***−0.01 m–l0.24−0.84**−0.010.03−0.000.02−0.110.07−0.17−0.14 s–i0.130.76***0.13−0.090.02−0.12−0.03−0.10−0.46**−0.01 lusal wear of UM1−0.13−0.230.02−0.04−0.290.17−0.090.68**0.040.21 The sample size is 33. The cumulative proportion of the variances of the ten principal components is 81.57%. p.v.: principal value; a–p: direction cosine for the anterior-posterior axis; m–l: direction cosine for the medial-lateral axis; s–i: direction cosine for the superior-inferior axis.

* P＜0.05; *

* **P＜0.01; *P＜0.001, by a two-tailed bootstrap test.

Table 6.Principal component analysis of the correlations between the linearizedfirst principal values and their direction cosines at six craniofacial landmarks, i.e., ft, STH, i, SCH, g, and zm in the three right elements, and the degree of occlusal wear on the maxillary first molar in Indians.1 Variable2Factor loadingsTotal variance (%)PC IIIIIIIVVVIVIIVIIIIXX Node 5 (ft) of Element 1: 1st p.v.0.52−0.45−0.10−0.29−0.450.10−0.080.10−0.060.1683.08 a–p−0.35−0.120.710.080.260.12−0.070.10−0.300.0683.60 m–l0.380.49−0.180.15−0.20−0.460.05−0.260.26−0.0882.43 s–i0.18−0.33−0.600.11−0.090.01−0.08−0.27−0.06−0.46*81.82 Node 6 (STH) of Element 1: 1st p.v.0.34−0.13−0.68−0.27−0.030.17−0.210.15−0.080.2382.16 a–p−0.570.220.04−0.330.55−0.07−0.10−0.150.13−0.1886.67 m–l0.420.110.410.17−0.20−0.200.54*−0.18−0.230.0184.28 s–i0.46−0.40−0.030.25−0.350.03−0.360.140.23−0.0176.40 Node 3 (i) of Element 2: 1st p.v.0.17−0.620.09−0.080.130.220.38−0.210.13−0.0871.03 a–p−0.77−0.020.02−0.10−0.31−0.25−0.100.050.23−0.0382.53 m–l0.450.360.510.16−0.190.07−0.380.07−0.260.0487.42 s–i0.38−0.480.02−0.010.330.410.33−0.230.030.2085.66 Node 8 (SCH) of Element 2: 1st p.v.0.26−0.150.25−0.510.060.02−0.140.430.36−0.2983.74 a–p−0.30−0.410.43−0.44−0.36−0.11−0.00−0.320.08−0.0189.01 m–l−0.410.09−0.30−0.370.040.47−0.18−0.340.080.3086.62 s–i0.040.44−0.600.280.39−0.050.170.20−0.120.0887.27 Node 1 (g) of Element 3: 1st p.v.0.01−0.450.040.330.50−0.22−0.340.08−0.070.1576.05 a–p0.160.67−0.14−0.54−0.14−0.01−0.07−0.15−0.100.2389.37 m–l−0.390.09−0.120.27−0.260.480.350.400.09−0.1886.82 s–i−0.09−0.50−0.180.440.23−0.33−0.25−0.240.120.0979.36 Node 7 (zm) of Element 3: 1st p.v.0.15−0.190.16−0.240.19−0.530.290.280.280.4389.18 a–p−0.270.130.220.57−0.170.42−0.080.020.390.2990.73 m–l0.480.100.40−0.190.430.23−0.29−0.05−0.07−0.1979.30 s–i−0.30−0.47−0.31−0.310.09−0.140.140.31−0.32−0.0474.77 Occlusal wear of UM1−0.54−0.35−0.030.10−0.44−0.14−0.11−0.02−0.42*0.0984.06 Total contribution (%)14.38 12.99 11.61 9.178.687.026.004.914.564.0083.34 Cumulative proportion (%)14.38 27.38 38.99 48.15 56.84 63.86 69.86 74.77 79.33 83.34 83.34 1 The sample size is 35. The number of principal components shown here was determined so that the cumulative proportion of the variances of the principal components exceeded 80%. 2 p.v.: principal value; a–p: direction cosine for the anterior-posterior axis; m–l: direction cosine for the medial-lateral axis; s–i: direction cosine for the superior-inferior axis. * P＜0.05; ** P＜0.01; ***P＜0.001, by a two-tailed bootstrap test.

ble 7.Rotated solution of the first ten principal components extracted from the correlations between the linearizedfirst principal values and their direction cosines at six craniofacial landmarks, i.e., ft, STH, i, SCH, g, and zm in the three right elements, and the degree of occlusal wear on the maxillary first molar in Indians.1 Variable2Factor loadings Fac IIIIIIIVVVIVIIVIIIIXX e 5 (ft) of Element 1: 1st p.v.0.81*0.04−0.07−0.22−0.10−0.240.200.000.100.05 a–p−0.360.300.19−0.290.110.17−0.040.66***−0.080.14 m–l0.030.080.230.14−0.09−0.00−0.22−0.82***−0.080.03 s–i0.24−0.23−0.060.100.25−0.330.19−0.270.01−0.64** e 6 (STH) of Element 1: 1st p.v.0.53−0.05−0.520.38−0.02−0.340.07−0.070.05−0.03 a–p−0.82*−0.02−0.34−0.070.06−0.13−0.100.060.190.02 m–l0.080.200.70***−0.09−0.27−0.020.25−0.18−0.310.17 s–i0.720.090.07−0.110.330.180.00−0.120.23−0.13 e 3 (i) of Element 2: 1st p.v.0.09−0.130.10−0.240.12−0.070.77***0.080.11−0.04 a–p−0.26−0.56−0.15−0.430.040.13−0.47*0.060.020.04 m–l0.270.75**0.27−0.03−0.150.20−0.320.04−0.05−0.01 s–i0.150.15−0.070.060.100.010.88***0.11−0.040.06 e 8 (SCH) of Element 2: 1st p.v.0.120.140.01−0.18−0.12−0.150.030.070.84***0.16 a–p−0.02−0.13−0.05−0.92***−0.06−0.100.070.09−0.000.08 m–l−0.17−0.08−0.85***−0.11−0.200.090.090.06−0.19−0.09 s–i−0.18−0.13−0.070.87***−0.00−0.08−0.09−0.14−0.160.00 e 1 (g) of Element 3: 1st p.v.−0.010.150.000.120.80***−0.060.050.24−0.000.13 a–p−0.040.29−0.370.08−0.62**−0.22−0.27−0.33−0.130.19 m–l−0.02−0.52*0.100.22−0.350.45−0.010.350.09−0.28 s–i0.02−0.15−0.03−0.040.85***0.000.08−0.12−0.17−0.04 e 7 (zm) of Element 3: 1st p.v.0.04−0.150.15−0.030.14−0.180.12−0.100.190.86*** a–p0.01−0.07−0.080.000.070.93***−0.040.09−0.12−0.01 m–l−0.100.79***0.020.020.00−0.080.190.070.34−0.06 s–i0.04−0.46*−0.100.010.10−0.56**0.040.45*0.050.06 lusal wear of UM10.15−0.39−0.01−0.380.15−0.10−0.320.40−0.45*−0.15 The sample size is 35. The cumulative proportion of the variances of the ten principal components is 83.34%. p.v.: principal value; a–p: direction cosine for the anterior-posterior axis; m–l: direction cosine for the medial-lateral axis; s–i: direction cosine for the superior-inferior axis.

* P＜0.05; *

* **P＜0.01; *P＜0.001, by a two-tailed bootstrap test.

Table 8.Principal component analysis of the correlations between the linearizedfirst principal values and their direction cosines at six craniofacial landmarks, i.e., ft, STH, i, SCH, g, and zm in the three left elements, and the degree of occlusal wear on the maxillary first molar in Indians.1 Variable2Factor loadingsTotal variance (%)PC IIIIIIIVVVIVIIVIIIIXX Node 5 (ft) of Element 1: 1st p.v.−0.21−0.76−0.26−0.070.330.210.090.04−0.180.0990.05 a–p0.360.27−0.280.66−0.110.24−0.030.210.070.31*93.97 m–l0.48−0.160.56−0.23−0.02−0.21−0.220.25−0.20−0.0381.25 s–i−0.500.340.290.11−0.030.070.21−0.350.28−0.44*91.60 Node 6 (STH) of Element 1: 1st p.v.−0.37−0.31−0.51−0.210.360.030.06−0.02−0.48*−0.0390.79 a–p0.270.73−0.410.21−0.10−0.000.08−0.110.100.0385.66 m–l0.42−0.160.500.11−0.04−0.35−0.31−0.06−0.27−0.2381.06 s–i−0.50−0.270.290.330.290.080.18−0.050.290.1974.98 Node 3 (i) of Element 2: 1st p.v.0.38−0.35−0.150.110.57*0.150.10−0.020.14−0.3277.81 a–p−0.350.070.460.36−0.020.050.55*0.15−0.27−0.1088.13 m–l−0.53−0.18−0.08−0.32−0.18−0.30−0.190.060.19−0.0361.15 s–i0.65−0.01−0.36−0.080.290.18−0.400.070.23−0.1391.68 Node 8 (SCH) of Element 2: 1st p.v.−0.32−0.45−0.210.410.12−0.37−0.13−0.240.070.1275.16 a–p0.14−0.630.290.08−0.520.380.01−0.140.05−0.0894.29 m–l−0.24−0.140.460.250.43−0.21−0.27−0.090.130.42*85.59 s–i−0.220.73−0.20−0.180.41−0.180.080.25−0.11−0.0193.55 Node 1 (g) of Element 3: 1st p.v.0.57−0.15−0.160.280.05−0.190.44−0.27−0.240.0982.50 a–p−0.490.01−0.31−0.18−0.430.43−0.110.03−0.120.1579.34 m–l−0.420.200.060.490.18−0.12−0.130.58**−0.01−0.2693.08 s–i0.560.160.17−0.320.30−0.000.38−0.280.120.0879.85 Node 7 (zm) of Element 3: 1st p.v.0.10−0.18−0.250.71−0.010.18−0.29−0.19−0.10−0.2783.83 a–p0.08−0.430.07−0.240.200.350.200.440.34−0.0877.19 m–l0.18−0.33−0.250.03−0.26−0.59*0.210.160.300.0878.04 s–i−0.220.390.39−0.130.350.34−0.34−0.38−0.040.1087.21 Occlusal wear of UM10.370.110.450.14−0.000.340.070.32−0.100.2164.67 Total contribution (%)15.13 13.57 10.78 9.107.877.005.995.674.333.8583.30 Cumulative proportion (%)15.13 28.70 39.49 48.59 56.45 63.46 69.45 75.12 79.45 83.30 83.30 1 The sample size is 35. The number of principal components shown here was determined so that the cumulative proportion of the variances of the principal components exceeded 80%. 2 p.v.: principal value; a–p: direction cosine for the anterior-posterior axis; m–l: direction cosine for the medial-lateral axis; s–i: direction cosine for the superior-inferior axis. *P＜0.05; ** P＜0.01; ***P＜0.001, by a two-tailed bootstrap test.

ble 9.Rotated solution of the first ten principal components extracted from the correlations between the linearizedfirst principal values and their direction cosines at six craniofacial landmarks, i.e., ft, STH, i, SCH, g, and zm in the three left elements, and the degree of occlusal wear on the maxillary first molar in Indians.1 Variable2Factor loadings Fac IIIIIIIVVVIVIIVIIIIXX e 5 (ft) of Element 1: 1st p.v.0.02−0.28−0.14−0.090.18−0.080.220.02−0.82***0.20 a–p0.160.02−0.220.86***0.03−0.13−0.120.210.210.01 m–l0.07−0.090.86***0.02−0.04−0.020.20−0.110.08−0.03 s–i−0.500.01−0.34−0.420.180.34−0.120.090.450.03 e 6 (STH) of Element 1: 1st p.v.−0.000.19−0.21−0.210.040.03−0.090.06−0.87***−0.08 a–p0.170.41−0.350.380.03−0.02−0.34−0.080.42−0.31 m–l0.01−0.180.82***−0.020.17−0.00−0.240.030.140.03 s–i−0.37−0.13−0.26−0.070.110.070.180.12−0.050.68*** e 3 (i) of Element 2: 1st p.v.0.18−0.060.030.090.79***−0.030.20−0.09−0.230.04 a–p−0.91***0.010.040.140.010.050.060.120.010.07 m–l0.070.01−0.11−0.62***−0.32−0.180.050.22−0.060.13 s–i0.78***0.050.080.230.44*0.030.13−0.020.03−0.18 e 8 (SCH) of Element 2: 1st p.v.0.02−0.16−0.16−0.160.12−0.31−0.390.21−0.270.54* a–p−0.09−0.95***0.090.02−0.04−0.030.14−0.020.00−0.07 m–l−0.030.060.220.00−0.030.17−0.030.040.010.88*** s–i−0.060.93***−0.13−0.03−0.060.170.010.060.03−0.12 e 1 (g) of Element 3: 1st p.v.−0.12−0.090.110.410.35−0.38−0.34−0.47−0.14−0.09 a–p0.04−0.21−0.48*−0.08−0.56**0.200.040.23−0.21−0.25 m–l−0.290.360.030.080.10−0.030.090.81***0.070.15 s–i0.040.160.130.090.300.060.14−0.78***0.16−0.06 e 7 (zm) of Element 3: 1st p.v.0.12−0.35−0.120.320.420.05−0.45*0.45*−0.070.02 a–p0.05−0.19−0.04−0.030.23−0.090.81***−0.00−0.150.01 m–l0.10−0.050.03−0.12−0.00−0.86***−0.01−0.060.080.07 s–i0.040.140.00−0.08−0.060.86***−0.07−0.120.130.26 lusal wear of UM1−0.14−0.090.330.56**−0.060.200.35−0.060.170.00 The sample size is 35. The cumulative proportion of the variances of the ten principal components is 83.30%. p.v.: principal value; a–p: direction cosine for the anterior-posterior axis; m–l: direction cosine for the medial-lateral axis; s–i: direction cosine for the superior-inferior axis.

* P＜0.05; *

* **P＜0.01; *P＜0.001, by a two-tailed bootstrap test.

Table 10. Principal component analysis of the correlations between the linearizedfirst principal values and their direction cosines at six craniofacial landmarks, i.e., ft, STH, i, SCH, g, and zm in the three right elements, and age in African-Americans.1 Variable2Factor loadingsTotal variance (%)PC IIIIIIIVVVIVIIVIIIIX Node 5 (ft) of Element 1: 1st p.v.−0.340.44***−0.120.39***−0.54***0.020.26**−0.24**0.0489.91 a–p0.72***−0.050.270.09−0.32−0.270.01−0.120.0479.47 m–l−0.320.32−0.340.160.37−0.09−0.53*−0.010.2382.10 s–i−0.67***−0.510.10−0.250.010.100.010.14−0.0081.15 Node 6 (STH) of Element 1: 1st p.v.−0.53*0.41***−0.23**0.26***−0.46***−0.110.25**−0.110.0686.92 a–p0.38*−0.490.36−0.13−0.24−0.20−0.38*−0.290.1588.23 m–l0.080.19−0.62−0.420.200.120.22−0.250.33*87.18 s–i−0.52**0.220.250.41−0.090.280.030.30*−0.2177.49 Node 3 (i) of Element 2: 1st p.v.0.360.23*0.31***−0.04−0.060.47***−0.07−0.050.64***92.21 a–p0.28−0.06−0.480.13−0.34−0.47−0.05−0.25−0.0473.83 m–l0.01−0.000.41−0.69*−0.08−0.200.040.21−0.0673.24 s–i−0.30−0.060.450.310.150.62**0.00−0.230.0585.60 Node 8 (SCH) of Element 2: 1st p.v.−0.110.69***0.11−0.44**−0.29*0.10−0.170.080.0082.43 a–p0.75***0.12−0.20−0.030.010.310.060.08−0.1975.80 m–l0.00−0.48*−0.550.210.300.150.03−0.060.1371.21 s–i−0.74***0.050.200.100.07−0.320.03−0.180.1275.67 Node 1 (g) of Element 3: 1st p.v.−0.42−0.57***−0.22−0.18−0.31**0.23**0.21**−0.120.1180.30 a–p0.60**0.420.360.33−0.020.080.240.110.1086.32 m–l−0.300.410.08−0.010.66**−0.390.08−0.09−0.0186.50 s–i−0.19−0.52−0.31−0.25−0.340.34−0.230.01−0.1576.78 Node 7 (zm) of Element 3: 1st p.v.−0.14−0.36***0.18*−0.30***0.03−0.27***0.59***0.28**0.34***88.68 a–p0.070.52−0.51−0.400.040.240.07−0.06−0.1377.43 m–l−0.43**0.110.54−0.26−0.06−0.00−0.17−0.47*−0.0481.15 s–i−0.08−0.29−0.170.55*−0.19−0.19−0.270.39*0.2980.23 Age−0.300.49*−0.17−0.33−0.36−0.05−0.320.360.2087.78 Total contribution (%)17.15 14.02 11.37 9.787.957.345.494.734.0881.90 Cumulative proportion (%)17.15 31.17 42.53 52.31 60.26 67.60 73.10 77.83 81.90 81.90 1 The sample size is 27. The number of principal components shown here was determined so that the cumulative proportion of the variances of the principal components exceeded 80%. 2 p.v.: principal value; a–p: direction cosine for the anterior-posterior axis; m–l: direction cosine for the medial-lateral axis; s–i: direction cosine for the superior-inferior axis. *P＜0.05; ** P＜0.01; *** P＜0.001, by a two-tailed bootstrap test.

ble 11. Rotated solution of the first nine principal components extracted from the correlations between the linearizedfirst principal values and their direction cosines at six craniofacial landmarks, i.e., ft, STH, i, SCH, g, and zm in the three right elements, and age in African-Americans.1 Variable2Factor loadings Fac IIIIIIIVVVIVIIVIIIIX e 5 (ft) of Element 1: 1st p.v.0.040.100.010.93***0.080.06−0.090.050.04 a–p0.33−0.020.020.01−0.40−0.70***0.120.16−0.04 m–l0.150.14−0.38−0.080.420.24−0.55*−0.29−0.01 s–i−0.64−0.010.00−0.160.46*0.240.270.180.02 e 6 (STH) of Element 1: 1st p.v.−0.030.19−0.070.85***0.240.19−0.01−0.03−0.11 a–p−0.16−0.070.01−0.310.03−0.84***−0.010.180.10 m–l−0.060.030.080.04−0.080.110.03−0.92***0.02 s–i−0.020.09−0.060.310.140.54*−0.090.56**0.18 e 3 (i) of Element 2: 1st p.v.0.190.19−0.07−0.04−0.23−0.220.03−0.180.84*** a–p0.01−0.10−0.200.31−0.15−0.47*−0.13−0.25−0.52*** m–l−0.030.50*0.34−0.360.09−0.130.44*0.09−0.09 s–i−0.12−0.290.220.080.180.24−0.180.330.69*** e 8 (SCH) of Element 2: 1st p.v.0.110.82**0.270.15−0.010.09−0.11−0.100.11 a–p0.17−0.050.10−0.15−0.80***−0.05−0.14−0.160.02 m–l−0.32−0.57*−0.35−0.12−0.060.14−0.10−0.34−0.05 s–i0.000.010.010.250.81***0.130.080.12−0.04 e 1 (g) of Element 3: 1st p.v.−0.79***−0.19−0.000.190.13−0.000.28−0.100.05 a–p0.69***−0.010.020.13−0.48*−0.100.090.180.31* m–l0.56*−0.030.14−0.140.57**0.35−0.04−0.18−0.17 s–i−0.85***0.03−0.03−0.07−0.13−0.04−0.10−0.00−0.06 e 7 (zm) of Element 3: 1st p.v.−0.07−0.06−0.07−0.090.180.010.91***−0.08−0.01 a–p−0.000.340.270.11−0.290.32−0.21−0.57***−0.13 m–l−0.080.200.53*0.040.59*−0.18−0.100.180.24 s–i−0.09−0.10−0.83***0.100.05−0.08−0.030.26−0.05 −0.100.86***−0.230.150.100.14−0.08−0.13−0.03 The sample size is 27. The cumulative proportion of the variances of the nine principal components is 81.90%. p.v.: principal value; a–p: direction cosine for the anterior-posterior axis; m–l: direction cosine for the medial-lateral axis; s–i: direction cosine for the superior-inferior axis.

* ***P＜0.05; *P＜0.01; *P＜0.001, by a two-tailed bootstrap test.

Table 12. Principal component analysis of the correlations between the linearizedfirst principal values and their direction cosines at six craniofacial landmarks, i.e., ft, STH, i, SCH, g, and zm in the three left elements, and age in African-Americans.1 Variable2Factor loadingsTotal variance (%)PC IIIIIIIVVVIVIIVIIIIX Node 5 (ft) of Element 1: 1st p.v.−0.54*0.44**−0.240.30*−0.150.46***0.16−0.18**0.0291.85 a–p0.60***−0.44−0.150.220.050.250.16−0.36*−0.0685.43 m–l0.13−0.39−0.10−0.640.390.040.04−0.050.0574.76 s–i−0.250.220.340.41−0.25−0.00−0.170.50**0.33*84.29 Node 6 (STH) of Element 1: 1st p.v.−0.480.52***0.010.18−0.130.55***−0.03−0.070.0886.89 a–p0.66***−0.35−0.120.31−0.220.28−0.020.22−0.1185.16 m–l0.08−0.47−0.04−0.66*0.020.110.010.210.42**89.63 s–i−0.73***0.130.100.170.41*0.04−0.09−0.27*0.0484.53 Node 3 (i) of Element 2: 1st p.v.−0.29−0.66***−0.24***0.13*−0.36***0.17**0.17**0.15**−0.0280.11 a–p0.55**0.150.030.290.400.20−0.310.00−0.3279.74 m–l−0.07−0.33−0.01−0.220.230.64**−0.410.090.2585.89 s–i−0.32−0.250.20−0.09−0.67*−0.220.44*−0.08−0.0891.40 Node 8 (SCH) of Element 2: 1st p.v.−0.66**−0.26−0.10−0.170.22*0.30**0.110.30*−0.39**93.07 a–p−0.59***−0.35−0.040.270.25−0.44**−0.18−0.080.1686.00 m–l0.12−0.32−0.310.21−0.250.340.32−0.390.2977.66 s–i0.44*0.680.16−0.32−0.100.310.05−0.07−0.0289.66 Node 1 (g) of Element 3: 1st p.v.−0.06−0.060.80***−0.05−0.180.26*−0.10−0.24*−0.0181.21 a–p−0.16−0.25−0.72*0.310.050.13−0.310.080.0482.27 m–l−0.250.39−0.48−0.51−0.07−0.000.02−0.30−0.1079.80 s–i0.23−0.060.76*0.240.190.130.140.000.1578.54 Node 7 (zm) of Element 3: 1st p.v.−0.25−0.39***0.46***−0.40***−0.11*0.18**−0.18**−0.24***−0.13*74.21 a–p0.13−0.350.060.420.50*0.060.49*0.05−0.0181.83 m–l−0.06−0.460.090.03−0.620.10−0.430.08−0.3089.05 s–i0.41*0.53−0.33−0.19−0.270.030.070.290.1176.32 Age−0.310.080.12−0.210.260.300.490.48*−0.1781.66 Total contribution (%)15.58 14.37 11.07 10.15 9.217.726.255.593.7183.64 Cumulative proportion (%)15.58 29.95 41.02 51.17 60.37 68.09 74.34 79.93 83.64 83.64 1 The sample size is 27. The number of principal components shown here was determined so that the cumulative proportion of the variances of the principal components exceeded 80%. 2 p.v.: principal value; a-p: direction cosine for the anterior-posterior axis; m–l: direction cosine for the medial-lateral axis; s–i: direction cosine for the superior-inferior axis. * P＜0.05; ** P＜0.01; ***P＜0.001, by a two-tailed bootstrap test.

ble 13. Rotated solution of the first nine principal components extracted from the correlations between the linearizedfirst principal values and their direction cosines at six craniofacial landmarks, i.e., ft, STH, i, SCH, g, and zm in the three left elements, and age in African-Americans.1 Variable2Factor loadings Fac IIIIIIIVVVIVIIVIIIIX e 5 (ft) of Element 1: 1st p.v.0.04−0.02−0.140.16−0.110.92***0.05−0.01−0.13 a–p0.83***0.060.06−0.030.22−0.21−0.05−0.200.16 m–l0.03−0.040.02−0.560.02−0.40*0.14−0.46**−0.18 s–i−0.28−0.020.060.06−0.090.23−0.070.83***0.02 e 6 (STH) of Element 1: 1st p.v.−0.140.100.06−0.000.010.90***0.010.11−0.10 a–p0.63***0.33−0.11−0.000.25−0.28−0.350.280.02 m–l0.020.10−0.01−0.80−0.31−0.370.01−0.07−0.08 s–i−0.27−0.65***0.120.010.070.51**0.22−0.10−0.11 e 3 (i) of Element 2: 1st p.v.0.42−0.28−0.23−0.16−0.440.01−0.440.11−0.25 a–p0.170.160.040.150.84***−0.10−0.010.010.04 m–l0.11−0.090.07−0.81**0.290.20−0.200.04−0.10 s–i0.07−0.030.220.26−0.84***−0.03−0.28−0.01−0.09 e 8 (SCH) of Element 2: 1st p.v.−0.15−0.35−0.10−0.18−0.060.21−0.24−0.16−0.78*** a–p−0.18−0.87***−0.160.01−0.14−0.040.040.110.08 m–l0.75***0.00−0.10−0.13−0.290.240.02−0.090.20 s–i−0.160.81*0.260.020.200.200.19−0.150.10 e 1 (g) of Element 3: 1st p.v.−0.03−0.010.85***−0.08−0.040.14−0.210.110.07 a–p0.23−0.30−0.72**−0.160.180.20−0.250.030.06 m–l−0.320.20−0.31−0.05−0.180.310.08−0.64***0.06 s–i0.18−0.030.71***0.020.17−0.120.220.39*−0.04 e 7 (zm) of Element 3: 1st p.v.−0.10−0.220.57−0.34−0.16−0.04−0.38−0.26−0.06 a–p0.57*−0.320.070.130.16−0.190.390.15−0.37 m–l0.04−0.060.07−0.05−0.14−0.08−0.91***0.100.09 s–i−0.130.76−0.370.04−0.010.010.120.080.10 −0.100.110.07−0.09−0.100.110.210.06−0.84*** The sample size is 27. The cumulative proportion of the variances of the nine principal components is 83.64%. p.v.: principal value; a–p: direction cosine for the anterior-posterior axis; m–l: direction cosine for the medial-lateral axis; s–i: direction cosine for the superior-inferior axis.

* P＜0.05; *

* **P＜0.01; *P＜0.001, by a two-tailed bootstrap test.