Multivariate analysis and the study of form, with special reference to canonical variate analysis

Abstract

SYNOPSIS. This paper presents a simple, geometric, largely intuitive introduction to the use of multivariate analysis for the study of biological form. Rather than presenting rigorous mathematical formulations of the theory and practice of statistics, the emphasis is on multivariate analysis as a descriptive, data-analytic approach which represents the quantitative version of classical comparative anatomy. One method-canonical variate analysis-is chosen for special attention because of its wide applicability to problems in which multidimensional data are used to compare differences between two, several, or many populations with proper regard for individual variation within the populations. The theory, practice, and utility of canonical variate analysis are presented by way of simple, bivariate examples. Particular attention is given to how the results of canonical variate analysis are affected by alterations in the within-group dispersion when the relationships among groups are held constant. Although the discussion focuses on canonical variate analysis, many statements transfer directly or with appropriate modification to the use of other multivariate procedures in comparative morphology. ©1980 by the American Society of Zoologists.