Statistical Methods for Comparison of Forms - An Invariant Approach to Statistical Analysis of Shapes - page 164

procedures can have smaller power as compared to some
other testing procedures. As pointed out here, and in the
original papers, neither EDMA-I or II are the uniformly
most powerful (UMP) tests. We never claimed EDMA-I or
EDMA-II to be UMP tests. Like most informed statisti-
cians, we are aware of the fact that tests in multivariate
analysis are seldom uniformly best; that is, they are not
the most powerful alternative in every possible situation.
Just as EDMA-based tests have smaller power in certain
testing situations, Procrustes-based tests have smaller
power in other situations. This finding alone does not
make either testing procedure (or any alternative!) unde-
sirable.

b) Rohlf's claim that the EDMA-II procedure is invalid stems
from an uninformed application of Step 5 in EDMA-II (see
above). Rohlf has fallen prey to the error of blind statisti-
cal testing that was pointed out in the original paper by
Lele and Cole (1996), and that we illustrate to the readers
of this monograph by way of an example (see Section 4.1.2,
Analysis of example data sets). EDMA-II, though not
UMP, is currently the only test that can be applied when
the covariance matrices for two populations are different.

c) Rohlf chooses a particularly unrealistic covariance struc-

ture, namely isotropic covariance, to conduct his
simulations. It has been shown that the Procrustes esti-
mators of mean form, mean shape, and covariance are
patently wrong for any covariance structure other than
isotropic (Lele, 1993; Kent and Mardia, 1997). What is obvi-
ous to statisticians, but perhaps less clear to biologists, is
that statistical inference procedures that use these erro-
neous estimators are not statistically valid. Rohlf (2000)
ignores this important issue and chooses to concentrate on
the non-UMP nature of the shape comparison tests.