Testing Proportionality of Covariance Matrices

Abstract

The problem of comparing the proportionality of covariance matrices often arises in genetic experiments. Knowledge of nonproportionality of covariance matrices is useful in selection work and in genetic interpretations. In developing a test of significance for this contrast, the likelihood ratio criterion was used. Likelihood ratio tests were obtained for two sets and for three sets of independent variance-covariance matrices. The test for $r$ independent covariances was indicated and some unsolved problems were cited.