Power of Tests for Equality of Covariance Matrices

Abstract

In this paper a Monte Carlo study of four test statistics used to test the null hypothesis that two or more multivariate normal populations have equal covariance matrices is presented. The statistics −2 In λ, −2 In W, −2ρ2 In λ and −2ρ2 ln W, where λ is the likelihood ratio criterion and W is Bartlett's modification of λ, are investigated. The reslllts indicate that for small samples the actual significance levels of the first, two statistics are somewhat greater than the nominal significance levels set, whereas for the latter two statistics the actual significance levels are close to the nominal levels. For these test statistics, −2ρ P 1 In h and −2ρ2 In W, the power is seen to be essentially identical; fnrther it increases as the sample size increases, as the inequality of the covariance matrices increases, and as the number of variates increases. Also, their power is seen to be a concave function of the number of populations.