A new test for multivariate analysis of variance with arbitrary covariance matrices: a computational approach test

In this study, we propose a new test based on the computational approach test (CAT) for testing k normal mean vectors when the covariance matrices are unknown and arbitrary. One of the key advantages of CAT is that it does not require explicit knowledge of the sampling distribution of the test statistic, which is particularly beneficial in complex hypothesis-testing scenarios. To assess the efficiency of the proposed test, we conducted an extensive Monte Carlo simulation study. The simulation results indicate that the proposed test consistently outperforms several recently discussed tests in the literature. Additionally, we provide a real data example to demonstrate the practical applicability of the proposed method.