Graphical Exploration in Comparing Variance Matrices

Abstract

A graphical technique for comparing variance-covariance matrices of several populations is proposed. These display each population's variance-covariance configuration by projecting it onto the plane of closest fit, i.e., along the first two principal axes. It is shown how to construct these h-plots and inspect them for linear combinations of variables on which the populations differ. It is further shown how, under normality assumptions, one may use the h-plots to approximate simultaneous tests of significance on the variance comparisons. An illustration is examined in detail to show the practical usefulness of the proposed technique for data analysis and testing.