Comparison of Multivariate Means across Groups with Ordinal Dependent Variables: A Monte Carlo Simulation Study - Finch, W. Holmes (Frontiers in Applied Mathematics and Statistics, 2016)
Multivariate analysis of variance (MANOVA) is a widely used technique for simultaneously comparing means for multiple dependent variables across two or more groups. MANOVA rests on several assumptions, including that of multivariate normality. Much prior research has investigated the performance of standard MANOVA with continuous, nonnormally distributed variables. However, very little work has examined its performance when the dependent variables are ordinal in nature. Therefore, the current study was designed to investigate the performance of standard MANOVA with ordinal dependent variables, and to compare it with several alternatives that might prove superior in this context. Results of the simulation study demonstrated that methods based on ranks, and spatial ranks and signs were optimal in terms of controlling the Type I error rate and maintaining reasonably high power. All of the methods considered here were applied to an existing dataset, and implications of the study results for practice are discussed.