The Effectiveness of Methods for Analyzing Multivariate Factorial Data

A Monte Carlo simulation was used to examine the effectiveness of univariate analysis of variance (ANOVA), multivariate analysis of variance (MANOVA), and multiple indicator structural equation (MISE) modeling to analyze data from multivariate factorial designs. The MISE method yielded downwardly biased standard errors for the univariate parameter estimates in the small sample size conditions. In the large sample size data conditions, the MISE method outperformed MANOVA and ANOVA when the covariate accounted for variation in the dependent variable and variables were unreliable. With multivariate statistical tests, MANOVA outperformed the MISE method in the Type I error conditions and the MISE method outperformed MANOVA in the Type II error conditions. The Bonferroni methods were overly conservative in controlling Type I error rates for univariate tests, but a modified Bonferroni method had higher statistical power than the Bonferroni method. Both the Bonferroni and modified methods adequately controlled multivariate Type I error rates.