An Empirical Comparison of Three Indices of Variable Contribution in Multiple Group Discriminant Analysis

This paper is concerned with an empirical comparison of three proposed indices of predictor variable potency: (1) the scaled weights of the first Fisher-type discriminant function, (2) the total group estimates of the correlations between each predictor variable and the first Fishertype function, and (3) the within-groups estimates of the correlations between each predictor variable and the first Fisher-type function. It was found that given a single run of an experiment none of the indices were sufficiently reliable to be oc great practical value in identifying potent variables except when the total sample size was very large. AN EMPIRICAL COMPARISON OF THREE INDICES OF VARIABLE CONTRIBUTION IN MULTIPLE GROUP DISCRIMINANT ANALYSIS R. A. Fisher's original discriminatory technique is well known and involves the reduction of a set of p measures to a single (composite) measure, a "linear discriminant function" (LDF), Y wl X1 + w2 X2 + + w X P P The w i (i = 1, ..., p) are determined so as to maximize the ratio of the differences between the sample means of the Y-values to the standard error of this difference as estimated from the within-groups mean square. In analysis of variance terminology this is equivalent to finding the wi such that, for the Y-values, the ratio