Minimum sample size requirements for two-way MANOVA designs: An examination of effect size, power, alpha level, number of dependent variables, and power of the interaction effect

Multivariate Analysis of Variance (MANOVA) is a statistical technique used to evaluate differences among means for a set of dependent variables, given that there are two or more levels of at least one independent variable. The two-way MANOVA design is a commonly used model in the literature; however, few empirical studies deal with minimum sample size and power even for the one-way MANOVA design (See Ito, 1962; Lauter, 1978; Olson, 1974; Pillai & Jayachandran, 1967; and Stevens, 2002). In addition, the literature concerning the power of the interaction effect in two-way designs is almost non-existent. Cohen, Cohen, Aiken, and West (2003) argue the lack of statistical power for testing interaction effects, but only in a theoretical manner. Therefore, it is unknown to practitioners the actual power available for testing an interaction effect between two or more independent variables. The main purpose of this study was to determine minimum sample sizes for various two-way MANOVA designs based upon specific correlation matrices among dependent variables. A secondary purpose was to examine the power for testing interaction effects between two independent variables for these various two-way MANOVA models. Monte Carlo simulations were used to generate 10,000 data sets for 24 correlation matrices of various dimensions (i.e., 2, 3, 4, and 5). Results indicate that practitioners need to be aware of the interrelationships of effect size, power (for main effects and interaction effects), alpha levels, the type of correlation among dependent variables, and the number of dependent variables in the model.