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Associations among cranial traits.

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BRIEF COMMUNICATION
Associations among Cranial Traits
ROBERT A. BENFER
University of Missouri, Columbia, Missouri
ABSTRACT
Multivariate analysis of associations among seven cranial characteristics originally presented by Hertzog ('68) suggests that the appearance of the circumparietal accessory ossicles, parietal foramina, and form of the fronto-temporal
suture are largely independent of each other both within and across geographical races.
Hertzog ('68) has presented associations
of seven cranial characteristics judged by
presence or absence. Five sites where accessory ossicles occur, the presence of
parietal foramina, and the form of the
fronto-temporal suture were recorded for
366 crania and presented for the total
sample as well as by six geographic racial
subsamples. It was suggested that the
number of significant associations varies
racially. Hertzog also observed adjacent
sites to be more highly associated than
those further apart.
In order to examine possible racial differences in the pattern of appearance of
these seven characteristics, I converted
the contingency coefficients (presented in
table 2, Hertzog, '68) to standard Pearson
product moment correlation coefficients,
which in the case of two by two contingency tables are often called phi coefficients. I intended to use image analysis,
a variation of principle components analysis, to compare nonredundant dimensions
of variation among the subsamples. Image
analysis proceeds from a matrix of correlation coefficients to an image-covariance
matrix in which the squared multiple
correlation coefficients of each variable
with all the others are placed in the principle diagonal and the off-diagonal entries
are adjusted to reflect only shared variation (Guttman, '53). Principle axes analysis, to compare nonredundant dimensions
result in components reflecting no unique
variance. The program used was Factor,
a listing and writeup of which may be
found in Veldman ('67). Output includes
the amount of common, or shared, variance in the original correlation matrix.
Table 1 presents the percent common
variance and the trace of the imagecovariance matrix, which is the sum of
AM. J. PHYS. ANTHROP.,32: 463464.
the squared multiple correlation coefficients for each variable (the Polynesian
sample was not analyzed since lambda
ossicles in these crania are totally lacking). As can be seen from the table, the
percent common variation ranges from
4.74 to 11.29. The sums of the squared
multiple correlation coefficients are uniformly very low.
Apparently, while individual assessments
of probability of the contingency coefficients do reach traditional levels of sigmficance (although the comparisons are not
independent), the actual amount of shared
variation is very small; too small, in fact,
for meaningful comparisons of differences
across races. Therefore I do not present
the results of the principle axes analyses
as they are based on too little common
variation to be meaningful. Slight differences in pattern which may exist within
the 5 to 12% shared variation could be
explained by sexual dimorphism or age
changes related to the traits of interest
and differing in the subsamples.
Results of this analysis suggest that the
seven discontinuous cranial traits analyzed
by Hertzog are almost completely independent of each other, and racial variation
TABLE 1
Interrelationships among seven cranial characteristics, data from Hertzog ('68)
Per cent
shared
vanance
Total sample
Asian subsample
European subsample
Amerindian subsample
African subsample
Indian subsample
6.14
4.74
6.90
11.29
9.30
6.63
~~~~~f
c o ~ a ~ n ~ e
0.430
0.332
0.483
0.790
0.651
0.464
463
464
ROBERT A. BENFER
in their pattern of Occumence has not been
demonstrated.
LITERATURE CITED
Guttman, L. 1953 Image theory for the stmcture of quantitative variates. Psychometrika,
18: 277-296.
Hertzog, K. P. 1968 Associations between discontinuous cranial traits. Am. J. Phys. Anthrop.,
29: 3 9 7 4 0 3 .
Veldman, D. J. 1967 Fortran Programming for
the Behavorial Sciences. Holt, Rinehart and
Winston, New York.
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