Visualizing Tests for Equality of Covariance Matrices

TL;DR

This paper introduces graphical visualization methods, including extensions of data ellipsoids and HE plots, to assess the equality of covariance matrices in multivariate models, enhancing interpretability of statistical tests.

Contribution

It presents novel visual tools and extensions for data ellipsoids, HE plots, and Box's M test components to improve evaluation of covariance matrix equality in multivariate analysis.

Findings

Extended visualization techniques for covariance matrices.

Implementation in R packages 'heplots' and 'candisc'.

Demonstrated application with real data examples.

Abstract

This paper 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 _how_ groups differ in covariance and also suggests other visualizations and alternative test statistics. These methods are implemented and freely available in the **heplots** and **candisc** packages for R. Examples from the paper are available in supplementary materials.