MANOVA versus alternative methods

Abstract

Multivariate analysis of variance (MANOVA) is a powerful tool in analysing multivariate data of multi-factorial experiments. However one of the assumptions in MANOVA requires the data to be normally distributed. This study concerned with the violation of this assumption, particularly when the data are either moderately non-normal or extremely non-normal. Possible alternative methods of handling such data are (i) permutational MANOVA (PMANOVA) or (ii) analysis of distance (AoD). Both of these alternative methods were compared with MANOVA via Monte Carlo experiments using the power of tests. The experiments focussed on testing interaction effects by incorporating different data types (i.e. having multivariate normal distribution, moderately non-normal and extremely non-normal), three level of inter-variable correlations (low: 0.25, medium: 0.5 and high: 0.75), two designs (small: 3×3 and large: 7×7) and two sample sizes (2 and 5 replicates). Overall, the results revealed that irrespective of the data types and the level of inter-variable correlations MANOVA performed satisfactorily in situations having larger sample size (5 replicates). In these situations, no alternative method is necessary. However, in small design with high inter-variable correlations PMANOVA performed slightly better. In small samples (2 replicates), AoD outperformed both MANOVA and PMANOVA. This is especially true in situation having small sample (2 replicates), large design and highly correlated inter-variables.