Statistical Methods for Comparison of Forms - An Invariant Approach to Statistical Analysis of Shapes - page 122

CHAPTER 4
Statistical Methods for
Comparison of Forms
“In a very large part of morphology, our essential task lies in the com-
parison of related forms rather than in the precise definition of each....”
D'Arcy Thompson (1992)
The previous chapter presented our notation and method for repre-
senting the form of an object and mean form for a sample. In this
chapter, we turn to the comparison of forms and introduce our method,
Euclidean Distance Matrix Analysis, or EDMA (pronounced ed·ma). To
clarify our approach, we consider other methods for the comparison of
forms, all of which can be classified as either superimposition tech-
niques or deformation techniques. We then present the EDMA
approach to the comparison of forms, providing suggestions for inter-
preting the output of these analyses and statistical approaches.
Statistical testing of the equality of shapes is provided in keeping with
traditional aspects of statistics. Since the testing of similarity in
shapes provides little in the way of biological information, we de-
emphasize that aspect of statistical testing and stress the importance
of exploring and demonstrating local differences between forms using
EDMA output (i.e., the form difference matrices) and confidence inter-
val methods. Finally, we provide analyses of our example data sets in
order to clarify and solidify the ideas presented.
4.1 Introduction
When observing the form of any object, we may be struck with a curios-
ity about why the object looks the way it does and why it is different