Robustness and Comparison of Wilks’ Test Statistic for Two-Way MANOVA

Abstract

The classical Wilks’ statistic is mostly used to test hypotheses in the two way multivariate analysis of variance (MANOVA), which is highly sensitive to the effects of outliers. The non-robustness of test statistics based on normal theory has lead many researchers to study different options. In this paper, we presented a robust version of the Wilks’ test statistic based on highly robust and efficient is  reweighted minimum covariance determinant estimates (RMCD). Monte Carlo simulations are used to evaluate the performance of the test statistics under various distributions. In addition, type I error rate results and test power are considered as statistical tools for comparing test statistics.