Comparison of the Invariant Solutions to the Multivariate Behren-Fisher Problems

Abstract

Four of numerous solutions to multivariate Behrens-Fisher problem were selected for comparison. The four selected invariant solutions were; Yao, Johansen, James and Krishnamorrthy and Yu. Data were simulated to compare the four solutions under different distributions (Multivariate Beta, Multivariate Gamma and Multivariate Normal), sample sizes (N = 20, 30, 50, 100, 200, 400 and 600), number of variables (p = 2, 3 and 5) and for equal and unequal sample sizes. The comparisons were done at three levels of significance (alpha = 0.01, 0.025 and 0.05) using power of the test and type I error rate. The results showed that James procedure is better than all other procedures when p = 2 with small sample sizes, because it has second highest power with the lowest type I error rate. But when number of variables p = 3 or 4 and with large sample size, all the four procedures’ performances are the same.