Introduction - An Invariant Approach to Statistical Analysis of Shapes - page 7

These three axioms permeate our topic. We lack the contribution of a
classicist, but we hope that our collaboration has produced a cohesive
blend of mathematics and biology in a readable format that is of sci-
entific value. Our intent is to provide a clear synopsis of Euclidean
Distance Matrix Analysis (EDMA), one of several techniques within
the class of methods called “geometric morphometrics'' (Bookstein,
1978). Our goal is to produce a clear, uncomplicated discussion of
EDMA including simple examples that can be joined with a precise
presentation of the mathematical and statistical details if the reader
so chooses. The discussion will occur within a broader description of
alternative geometric morphometric methods in order to clarify certain
characteristics of EDMA.
Understanding morphometric techniques can be especially difficult
because statisticians and mathematicians often devise the methods,
because the methods are communicated in formats that do not always
include an explanation of the underlying principles and algorithms,
and because biologists, whose familiarity with statistics may only be
casual, eventually adopt the methods. We keep the novice morphome-
trician in mind as we write this volume. We do this by offering expla-
nations of the statistical logic and algorithms at varying levels of diffi-
culty. The first part of Chapters 2 through 4 contains intuitive expla-
nations with uncomplicated arguments of the underlying statistical
and mathematical ideas along with analyses of real biological data
sets. The second part of these chapters provides a fully rigorous, math-
ematical treatment of the statistical theory that underlies the meth-
ods. The data sets to be used throughout this topic are described below.
1.3 Description of the data sets
Three data sets that have been studied in previous publications (Corner
and Richtsmeier, 1991; Richtsmeier, Cheverud et al., 1993; Richtsmeier,
Valeri et al., 1998; Richtsmeier, Baxter et al., 2000) are used throughout
the topic to clarify methods and concepts as they are introduced. Any
number of examples could be used, but we present data sets with which
we have had experience in order to convey statistical and biological
observations. Our scientific interest has focused on craniofacial mor-
phology and growth, and our examples reflect that interest. Here, we
introduce these data sets in fair biological detail by providing basic
descriptions and background relevant to why the data sets are inter-
esting biologically. We provide information pertaining to the collection