Statistical power for repeated measures anova

Determining power a prior for univariate repeated measures (RM) ANOVA designs is a difficult and often excluded practice in the planning of experimental research. Complicated procedures and lack of accessibility to computer power programs are among some of the problems which have discouraged researchers from perforrning power analysis on these designs. Another more serious issue has been the lack of methods available for estimating power of designs with two or more R M factors. Due to uncertainties on how to compute an appropriate error term when more than one variance-covariance matrix exists, analytical methods for approximating power are currently restricted to R M designs with only one withinsubjects variable. The purpose of this study therefore, was to facilitate the process of power detennination by providing a series of power tables for ANOVA designs with one and two within-subject variables. A secondary objective was to investigate less well known power trends among ANOVA designs having heterogeneous (nonspherical) correlation matrices or two R M factors. Power was generated using analytical and Monte Carlo simulation methods for varying experimental conditions of sample size (5, 10 , 15, 20, 25 & 30), effect size (small, medium & large), alpha (.01, .05 & .10), correlation (.4 & .8), variance-covariance matrix patterns (constant, e=1.00 and trend, e<.56) and levels of R M (3, 6 & 9). Examination of power results revealed that under conditions of nonsphericity (trend matrix pattern), power was found to be greater at small effect sizes and lower at medium and large effect sizes compared to those values generated under conditions involving spherical (constant matrix) structures. Regarding designs with two R M factors, power of main effects tests was observed to be greatest for a given condition so long as the average correlation among trials of the pooled factor was equal to or below that of the main effects factor. For interaction tests of the same model, power was found to be greatest for a given condition when at least one factor had an average correlation across its trials equal to .80. From simulation results, the relationship between error variance and power across different correlation matrices of the two-way R M design was examined and approximations of the noncentrality parameter for each test of this model were derived.Education, Faculty ofKinesiology, School ofGraduat