A MONTE CARLO COMPARISON OF THE UNIVARIATE AND MULTIVARIATE METHODS FOR THE GROUPS BY TRIALS REPEATED MEASURES DESIGN

Computer simulation techniques were used to compare the power and probability of Type I error (u) for the usual univariate, adjusted univariate, and multivariate tests. These tests were studied under the following conditions: (a) hormal distribution with equal correlations among levels of the repeated factor, (b) normal distribution with unequal correlations among levels of the repeated factor, (c) skewed distribution with equal correlations among levels of the repeated factor, and (d) skewed distributions with unequal correlations among levels of the repeated factor. The experimental design which was simulated was a groups by trials repeated measures design, where "groups" and "trials" are the generic terms for the non-repeated and repeated factors, respectively. When sampling from a normal distribution with unequal correlation among trials, the multivariate tests were generally more powerful than the univariate tests. However, when the correlations among trials were equal, the univariate tests were more powerful. The (Y level for the usual univariate test was the only one to differ significantly from nominal u (.06). Non-normality had little effect on the results, with the exception that the (Y level increased considerably in the multivariate test for the trials effect.