EVALUATION OF HOTELLING T2 AND MULTIVARIATE ANALYSIS OF VARIANCE TESTS

Abstract

Multivariate analysis of variance (MANOVA) which comprises of Wilks' lambda, Pillai's trace, Lawley-Hotelling trace and Roy's largest root are compared with Hotelling T square when null hypothesis is true. Data were simulated to compare the five (5) test statistics under the two different distributions (Multivariate Gamma and Multivariate Normal), sample size (10, 30, 60, 90, 400, 500, 800 and 1000), number of variables p = 2 and equal and unequal sample size and variance covariance matrix. The comparisons were done at two levels of significant (alpha = 0.01 and 0.05) using power of the test and type I error rate. The results showed that Roy's largest root test statistic is better than all other test statistics considered when sample size are equal but Hotelling T square performed better for unequal sample size