ANOVA on principal component as an alternative to MANOVA

Abstract

With its strict assumptions, practitioners found difficulties in applying Multivariate Analysis of Variance (MANOVA) on their works. When normal assumption is partially fulfilled on multivariate responses, it does not guarantee that the responses are to be multivariate normal distributed simultaneously. To tackle this problem, we proposed a method by simply applying Analysis of Variance (ANOVA) on principal component (PC). The PC is a linear combination of the responses. Once all the responses are normally distributed, the PCS will also be. Accordingly, all we need is to ensure that the responses are to be partially normal distributed and the multivariate normal distribution is needless. The results of our data analysis indicated that our proposed method can be used as an alternative to MANOVA, especially when multivariate normal assumption could not be fully guaranteed.