Robust Test Statistics for O ne-Way Munlivariate Analysis of Variance (MANOVA) Model: Simulation Study


One-way multivariate analysis of variance (MANOVA) deals with testing the null hypothesis of equal mean vectors of two or more multivariate normal populations. The classical Wilks', Roy’s, Pillai’s, and Lawley-Hotelling statistics are used and well-known for testing the hypotheses in one-way MANOVA which are extremely sensitive to the influence of outliers. In this study the robust test statistics based on reweighted minimum covariance determinant (RMCD) estimator with Hampel weighted function have been proposed. Also, the approximate distributions for the robust test statistics have been constructed which are related directly with weights. The distributions of the proposed statistics differ from the classical one. Monte Carlo simulations are used to evaluate the performance of the test statistics under various distributions in terms of the simulated significance levels, its power functions and robustness. The powers of the robust and classical statistics are compared using size-power curves. The results show that, the robust test statistics are close to the classical test statistics in case of normal distribution for the data set. In the case of contaminated distribution, the P-value plots and size-power curves clearly show the advantage of the proposed robust test statistics over the classical statistics.