Approximate randomization tests for MANOVA
Description
Multivariate Analysis of Variance (MANOVA) is a commonly used statistical procedure for group comparison in behavioral research, however, the traditional parametric approach for MANOVA when there are more than two groups has Type I error rates that deviate from stated alpha (Olson, 1976) and may have poor power (Stevens, 1980). The approximate randomization test (ART), a nonparametric and computer intensive approach, has been recently recommended as a theoretically attractive alternative to parametric MANOVA (Edgington, 1987; Manly, 1991), but its performance relative to the parametric procedures has not been empirically investigated. The main purpose of this study is to evaluate the advantages, disadvantages, and feasibility of applying the ART for MANOVA using Monte Carlo methods. Results indicate that, contrary to the common belief, the ART in general yield Type I error rates similar in tendency and degree to that for parametric methods under assumption violations. Although the ART using composite z score as statistic recommended by Edgington (1987) is less biased compared to the parametric method under assumption violations, it may not test the same hypothesis tested by the parametric method. This study concludes that despite the theoretical attractiveness of the ART, none of the previously recommended statistics yields a satisfactory test for replacing the parametric MANOVA