Monte Carlo Simulation Study on the Power of Two-Sample Hotelling's Test

Abstract

Hotelling's T2 statistic is one of the multivariate tests that are based on certain fundamental assumptions, one of which is the multivariate normality. The test is usually applied to investigate the equality of means associated with two normal multivariate populations. The application of the test when the normality assumption is violated may affect the power of the test. In this paper, a Monte Carlo simulation is conducted to compare the exact powers of T2 based on multivariate normal and four multivariate non-normal populations. The results show insignificant differences in the average power performance between the normal and non-normal populations for both small and large sample sizes. It was also observed that the results from multivariate normal distribution do not show any unique performance from non-normal distributions when samples sizes are large.