Power comparisons of tests of equality of two covariance matrices based on four criteria

Abstract

Exact non-central c.d.f.'s of four criteria in the two-roots case are derived for tests of the hypothesis Σ1 = Σ2 against one-sided alternatives, where Σ1 and Σ2 are covariance matrices of two normal populations. The tests are based on Roy's largest root, and on Lawley-Hotelling's, Pillai's and Wilks's criteria. Powers of the last three criteria have been tabulated extensively, and power comparisons have been made between the three, and also with the largest root, whose powers have been tabulated elsewhere. In addition, powers of the largest root for large deviations are also given for the canonical correlation and multivariate analysis of variance cases, providing power oomparisonns with the other three criteria.