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 (n 1 : n 2 ), sample-size-to-variables ratio, and degree of heteroscedasticity. These tests are alternatives to Hotelling’s T 2 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, (n 1 + n 2 )/p ≥ 10, and 1:2 ≤ n 1 :n 2 ≤ 2:1. When (n 1 + n 2 )/p = 20, Yao’s test was robust when n 1 : n 2 was 5:1, 3:1, and 4:1 and p was 2, 6, and 10, respectively.