A Robust Comparison Powers of Four Multivariate Analysis of Variance Tests

Abstract

This paper compared the powers of four test statistics of Multivariate Analysis of Variance and test statistics include Lawley-Hotelling ,Pillai's trace, Roy’s largest root and Wilks' lambda. The R Statistics was employed to simulate the data used to compare the four test statistics under the Multivariate Gamma and Multivariate Normal distributions. The sample sizes utilized were 10, 20, 30, 40, 100, 200, 300, 400, 600, 700, 800 and 1000); Number of variables (p = 2, 3, and 4) equal and unequal samples and variance co-variance matrix were also used. The comparison were done at two levels of significance (α = 0.01 and 0.05) using power of the test. The results obtained indicated that the Roy’s largest Root test statistic is better than all other test statistic considered when p = g = 2 because it has the least powers. The result of the analysis further showed that when p = g = 3 and p = g = 4 the Wilks' lambda proved better than all other test statistics both for small and large sample sizes. The results equally showed that when the data are multivariate normal and Gamma with g =2 and p = 2 the power of the four test statistics from best to least is Roy’s largest root, followed Lawley’s trace = Pillae’s trace and the least is Wilks’ Lambda at significant levels of 0.01 and 0.05 for equal and unequal samples. More so, when data are multivariate normal as well as gamma and p= g = 3 and p=g=4, the power of the four statistics ranked from best to least is Wilks’ Lambda , Pillae’s trace = Lawley’s trace and Roy’s largest root respectively . From the findings, it is evidently obvious that Roy’s largest root should be applied when p=g=2 while Wilks’ Lambda be used when p=g=3 and p=g=4. This study will help researchers to plan studies with controlled probabilities of detecting a meaningful effect thereby giving conclusive results with maximum efficiency.