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FIGURE 12.5 Three-dimensional coordinate date from 20 cranial landmarks from 164 individuals (lateral view
with facial landmarks to the right and vault landmarks to the left): (a) before Procrustes superimposition and (b)
after Procrustes superimposition.
projected into the linear space tangent to the Procrustes hemisphere or nonparametric statis-
tical methods can be applied. Alternately, a linear statistical analysis, such as principal
component analysis, that approximates the curved shape space and reduces the dimension-
ality of the shape coordinates can be used. In some cases, the principal component scores will
illustrate differences among groups, both in scatter plots and in shape variation by visual-
izing shape change associated with scores along the principal component axes. The principal
component scores based on the shape coordinates can also be used for standard morpho-
metric analyses such as CVA, DFA, MANOVA or MANCOVA, regression, and R matrix
analysis with a program such as RMET (by John Relethford).
Group means can be visually compared by graphically displaying the coordinate config-
urations together so that differences in the locations of landmarks can be seen. Difference-
vector diagrams enhance this capacity by showing vectors extending from the location of
a landmark on one configuration (usually the group mean) to the homologous landmarks
of the other configuration (usually the other group mean) ( Slice, 2007 ). The direction and
magnitude of the differences can easily be appreciated from these graphical depictions of
shape variation. Figure 12.6 illustrates the superimposition of group means from samples
of Euro-American and African-American males from the Robert J. Terry Anatomical Skel-
etal Collection housed at the Smithsonian Institution's National Museum of Natural History
in Washington, D.C. The figure clearly shows variation in the location of certain landmarks
between the two group means.
The most obvious differences are in the vault, with the African-American mean having
more posteriorly oriented landmarks, particularly bregma, mastoideale, basion and lambda.
This suggests an overall elongated vault when compared to the more anterior position of
these landmarks in the Euro-American male mean. Additionally, the more laterally posi-
tioned landmarks mastoideale and asterion indicate a broader vault for the Euro-American
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