Type I Error Rates for Yao’s and James Tests of Equality of Mean Vectors Under VarianceCovariance Heteroscedasticity

Abstract

For Yao’s and James’ tests, Type I error rates were estimated for various combinations of the number of variables (p), samplesize ratio (n₁: n₂), sample-size-to-variables ratio, and degree of heteroscedasticity. These tests are alternatives to Hotelling’s T² and are intended for use when the variance-covariance matrices are not equal in a study using two independent samples. The performance of Yao’s test was superior to that of James’. Yao’s test had appropriate Type I error rates when p ≥ 10, (n₁ + n₂)/p ≥ 10, and 1:2 ≤ n₁:n₂ ≤ 2:1. When (n₁ + n₂)/p = 20, Yao’s test was robust when n₁: n₂ was 5:1, 3:1, and 4:1 and p was 2, 6, and 10, respectively.