Statistical Methods for Comparison of Forms - An Invariant Approach to Statistical Analysis of Shapes - page 163

4.9.3. Cautionary notes regarding hypothesis testing
for similarity of shape

1. We emphasize that statistical testing for equality of shape,

although a standard feature of most published analyses, is
overrated and rarely provides the information desired or
required by the scientist. This is because the answer given
from a statistical test is limited to either, “yes, the shapes are
the same” or “they are different.” What is generally needed is
the detection of those parts of the forms that are similar and
those that are different, along with a measure of this differ-
ence. Localization facilitates the formulation of informed
hypotheses about “why” or “how” two forms differ. Explan-
ation and discovery are our goals, not description. Our method
for the calculation of confidence intervals, in addition to the
exploration procedures described below, are tools designed for
studying the more subtle and meaningful aspects of form dif-
ference.

2. There are many different ways to test a hypothesis of equali-

ty of shape. Unfortunately, due to the nature of the problem,
there cannot be a single test that is 'best' in every situation.
By 'best' we mean the test that has the greatest statistical
power to detect a real shape difference (the probability of
rejecting a false null hypothesis). Simulation studies can be
misleading because they report the power of one test relative
to others in a specific situation . The problem is that one can
always find a situation where any particular test behaves
well. Due to the nature of biological data, simulation studies
cannot support the use of one test over the other in all, or even
most, situations. In the light of the above discussion we feel it
necessary to remark on the misleading nature of the com-
mentary on the EDMA testing procedures provided by James
Rohlf (2000). As we have pointed out, superimposition and
deformation approaches base their inference on non-identifi-
able parameters, which makes these approaches scientifically
and statistically problematic, and possibly undesirable.
Unfortunately, Rohlf (2000) provides a highly biased view of
shape analysis in his paper. The main flaws in his argument
are presented below.
a) Using simulations, Rohlf shows that the EDMA testing