Comparison of Some Robust Wilks’ Statistics for the One-Way Multivariate Analysis of Variance (MANOVA )

Abstract

The classicalWilks' statistic is mostly used to test hypothesesin the one-way multivariate analysis of variance (MANOVA), which is highly sensitive to the effects of outliers. The non-robustness of the test statistics based on normal theory has led many authors to examine various options.In this paper, we presented a robust version of the Wilks' statistic and constructed its approximate distribution.A comparison was made between the proposed statistics and some Wilks' statistics. The Monte Carlo studies are used to obtain performance assessment of test statistics in different data sets.Moreover, the results of the type I error rate and the power of test were considered as statistical tools to compare test statistics.The study reveals that, under normally distributed, the type I error rates for the classical and the proposedWilks' statistics are close to the true significance levels, and the power of the test statistics are so close. In addition, in the case of contaminated distribution, the proposed statistic is the best.