A Comparison of Some Test Statistics for Multivariate Analysis of Variance Model With Non-Normal Responses

Abstract

The Multivariate analysis of variance (MANOVA) is often used to model responses from more than one response variable on a single factor or a set of factors of interest. The existing statistical methods for MANOVA modelling generally assume that the set of responses, and by extension the model error term have a Gaussian distribution. However, in many real life situations, the vector of responses are not normally distributed, thereby rendering some of the existing methods inefficient, especially under small sample size situations. This study therefore, investigates, through Monte-Carlo studies, the behaviours of three of the existing techniques for performing MANOVA tests when normality assumption on the error term is violated. Two truncated test statistics for MANOVA testing on data with non-normal responses were developed from the existing test methods. The Monte-Carlo results showed that the original Roy’s test method and the two proposed truncated test statistics are relatively more efficient for MANOVA testing on data with inherent non-Gaussian responses under small sample sizes situations.

Keywords: MANOVA Tests, Non-normal error term, Wilks, Pillai, Roy’s statistics, Power