MANOVA

Vita.This dissertation combines interpretative techniques involved in principle components analysis and in the multivariate analysis of variance. Particular emphasis is given to the interpretation of eigenvectors as discriminant functions. Evaluations of techniques are based on a sampling study of the eigenvalues and eigenvectors of the W (to the negative 1st power) H matrix of the MANOVA and on some "live data" examples. Chapter I contains a brief review of the pertinent literature and a statement of the desirability of an investigation of interpretative techniques. Chapter II presents in concise form a description of the techniques of principal components analysis and of the multi-variate analysis of variance with an emphasis on the similarities of these two techniques. Chapter III presents the results of a sampling study designed to investigate the behavior of the eigenvalues and eigenvectors of the W (to the negative 1st power) H matrix of the multivariate analysis of variance under various relative constructions of the hypothesis and error matrices. Trivariate normal samples were generated for sample sizes (all having the same error degrees of freedom) with the treatment variance-covariance patterns including equal and unequal variances as well as the absence and the presence of covariance