"Quick and Easy" Formulae for Approximating Statistical Power in Repeated Measures ANOVA

Abstract

The determination of statistical power for a repeated measures experimental study is a necessary, but difficult and seldom done, calculation. The purpose of this study was to provide practical methods for the a priori determination of power for the repeated measures (RM) analysis of variance (ANOVA). Stepwise regression analysis procedures were used to derive 10 power approximation equations for the main and interaction effects of the 1-way RM, 2-way mixed and 2-way RM ANOVA designs. The theoretically correct power values were calculated using the program DATASIM (Bradley, 1988) for various levels of effect size, number of levels of each factor, sample size, and mean correlations among RM factor levels. Potvin and Schutz's (in press) equations for estimating the error variance were utilized for computing power for the 2-way RM ANOVA. The derived equations showed a high level of precision in approximating power (R² = .97 to .99, SEE = .0 12 to .035) with 9 to 16 predictor variables for the 1-way RM and the 2-way mixed designs. For the 2-way RM design, however, the levels of precision were relatively low for the main effect (R² = .66 and .81 for α levels .01 and .05, respectively), and the residuals of the regression equation for the interaction effect showed a nonlinear relation with the criterion variable. Recommendations are given for the practical usage of the derived equations, and examples for calculating power for each design are provided.