Biology Reference
In-Depth Information
FIGURE 6.15
Landmark coordinates, in partial Procrustes superimposition, for 119 squirrels from three geo-
graphic samples. Circles
western Michigan, gray squares
eastern Michigan, triangles
southern states.
5
5
5
condyloid processes (between landmarks 5 and 6
9). This dimension is highly variable
within samples, such that the variation is quite large relative to the differences between
means. Consequently, PC1 is unlikely to meet the criterion for an efficient discriminator
even though the differences on this axis might be statistically significant. Another axis that
has relatively less variation compared to the differences between means would be a better
discriminator.
Results of CVA will look different from those of PCA for two crucial reasons. First,
CVA is describing differences between groups, and the direction in which group means
are most different is not necessarily the direction in which individuals are most different.
Second, CVA does not simply rotate the original data to the axes that maximize the group
differences, it finds the axes that optimize between-group differences
relative
to within-
group variation and, in general, these axes will be different directions from the ones that
maximize between-group differences. In addition, optimization also involves rescaling
such that the new axes are scaled differently from the original axes and scaled differently
from each other. Consequently, distances and relative positions in CV space can be quite
different from distances and positions in the original data, and interpretations of results
can be counterintuitive.
Because there are only 3 sample groups, there can be only 2 CVs. The plot of scores on
those two axes (
Figure 6.17
) shows that it was possible to find two axes of differentiation,
that the 3 means are not collinear. The distributions also show more circular distributions
with much less overlap than was seen in the PC scores. Thus, different combinations of
