Speaker: Michael Friendly, York University, Brain, Quantitative Methods area, Department of Psychology

Title: Visualizing Tests for Equality of Covariance Matrices

Abstract: This talk explores a variety of topics related to the question of
testing the equality of covariance matrices in multivariate linear
models, particularly in the MANOVA setting. The main focus is on
graphical methods that can be used to address the evaluation of this
assumption.

We introduce some extensions of data ellipsoids,
hypothesis-error (HE) plots and canonical discriminant plots and
demonstrate how they can be applied to the testing of equality of
covariance matrices. Further, a simple plot of the components of Box's M
test is proposed that shows \emph{how} groups differ in covariance and
also suggests other visualizations and alternative test statistics. A
multivariate extension of Levene's test of homogeneity of variance is
also discussed, which leads to other novel visualizations for equality
of covariance matrices within the HE plot framework. These methods are
implemented and freely available in the heplots and
candisc packages for R.