Rotation of Canonical Variates in Multivariate Analysis of Variance

Abstract

A general discussion is undertaken to show how the rotation techniques of factor analysis can be used to clarify and interpret the results of multivariate analysis of variance and discriminant analysis. Two general methods of rotating are explained; direct rotation, where the variance of the canonical variates is attached to the canonical variate scores, and indirect rotation where the variance of the canonical variates is attached to the principal components of the hypothesis. Two reasons for rotating are discussed, one giving rise to a taxonomy of groups or levels of a multivariate analysis of variance, the other giving rise to a taxonomy of variables involved in a multivariate analysis of variance. Two examples are given: one, a particular variety of taxonomy of groups and the other, a taxonomy of variables or battery reduction scheme.