Statistical Methods for Comparison of Forms - An Invariant Approach to Statistical Analysis of Shapes - page 162

analyses, the user must be wary of outcomes and pay close attention to
data and distributions. The example analysis given later in this chap-
ter demonstrates this type of situation and its resolution.
Table 4.1 summarizes the differences and similarities between the
two methods for testing the hypothesis of similarity in shapes of forms
sampled from two populations.

Table 4.1. Tabulation of the salient characteristics of the two methods
for hypothesis testing using EDMA.

EDMA-I EDMA-II

Description and comparison of Description and comparison of

forms are coordinate system-free forms are coordinate system-free

Null hypothesis states that the Null hypothesis states that the

shapes are similar shapes are similar

Enables statistical determination Enables decomposition of

of differences due exclusively to statistically significant

scale or due to differences in form differences into differences in

shape and differences in scaling
factor (or “size”)

Mean form matrices are invariant Mean shape matrices are

to the choice of scaling factor dependent on the choice of

scaling factor

Assumes equality of the variance- Does not assume equality of the

covariance matrices for the two variance-covariance matrices

samples under consideration

Testing procedure cannot determine Testing procedure cannot

localized differences; confidence determine localized differences;

intervals for elements of the FDM

confidence intervals for elements

of the SDM have been developed

have been developed for

this purpose. for this purpose.