Statistical power for the two-factor repeated measures ANOVA

Determining a priori power for univariate repeated measures (RM) ANOVA designs with two or more within-subjects factors that have different correlational patterns between the factors is currently difficult due to the unavailability of accurate methods to estimate the error variances used in power calculations. The main objective of this study was to determine the effect of the correlation between the levels in one RM factor on the power of the other RM factor. Monte Carlo simulation procedures were used to estimate power for the A, B, and AB tests of a 2 x 3, a 2 x 6, a 2 x 9, a 3 x 3, a 3 x 6, and a 3 x 9 design under varying experimental conditions of effect size (small, medium, and large), average correlation (.4 and .8), alpha (.01 and .05), and sample size (n = 5, 10, 15, 20, 25, and 30). Results indicated that the greater the magnitude of the differences between the average correlation among the levels of Factor A and the average correlation in the AB matrix, the lower the power for Factor B (and vice versa). Equations for estimating the error variance of each test of the two-way model were constructed by examining power and mean square error trends across different correlation matrices. Support for the accuracy of these formulae is given, thus allowing for direct analytic power calculations in future studies.