Tests of Significance in Multivariate Analysis

Abstract

A unified approach to the problem is given, making use of the concept of analysis of dispersion in analogy with the analysis of variance for the univariate case. The matrix of mean products giving unbiased estimates of the variances and covariances is called the error matrix; that of mean products yielding unbiased estimates only under the null hypothesis, the matrix due to deviation from the hypothesis. The approp. test criterion is a root of a determinantal equation. Wilk''s A criterion is related to the set of roots. The problem of analysis of dispersion of 1 set of variables when the dispersion due to another set is removed is shown to depend also on A. A number of examples illustrating computational procedure are included.