Comparison of the Performance of Nonparametric and Parametric MANOVA Test Statistics when Assumptions Are Violated

Abstract

Abstract. Multivariate analysis of variance (MANOVA) is a useful tool for social scientists because it allows for the comparison of response-variable means across multiple groups. MANOVA requires that the observations are independent, the response variables are multivariate normally distributed, and the covariance matrix of the response variables is homogeneous across groups. When the assumptions of normality and homogeneous covariance matrices are not met, past research has shown that the type I error rate of the standard MANOVA test statistics can be inflated while their power can be attenuated. The current study compares the performance of a nonparametric alternative to one of the standard parametric test statistics when these two assumptions are not met. Results show that when the assumption of homogeneous covariance matrices is not met, the nonparametric approach has a lower type I error rate and higher power than the most robust parametric statistic. When the assumption of normality is untenable, the parametric statistic is robust, and slightly outperforms the nonparametric statistic in terms of type I error rate and power.