Testing treatment effects in repeated measures designs: trimmed means and bootstrapping

Non-normality and covariance heterogeneity between groups affect the validity of the traditional repeated measures methods of analysis, particularly when group sizes are unequal. A non-pooled Welch-type statistic (WJ) and the Huynh Improved General Approximation (IGA) test generally have been found to be effective in controlling rates of Type I error in unbalanced non-spherical repeated measures designs even though data are non-normal in form and covariance matrices are heterogeneous. However, under some conditions of departure from multisample sphericity and multivariate normality their rates of Type I error have been found to be elevated. Westfall and Young's results suggest that Type I error control could be improved by combining bootstrap methods with methods based on trimmed means. Accordingly, in our investigation we examined four methods for testing for main and interaction effects in a between- by within-subjects repeated measures design: (a) the IGA and WJ tests with least squares estimators based on theoretically determined critical values; (b) the IGA and WJ tests with least squares estimators based on empirically determined critical values; (c) the IGA and WJ tests with robust estimators based on theoretically determined critical values; and (d) the IGA and WJ tests with robust estimators based on empirically determined critical values. We found that the IGA tests were always robust to assumption violations whether based on least squares or robust estimators or whether critical values were obtained through theoretical or empirical methods. The WJ procedure, however, occasionally resulted in liberal rates of error when based on least squares estimators but always proved robust when applied with robust estimators. Neither approach particularly benefited from adopting bootstrapped critical values. Recommendations are provided to researchers regarding when each approach is best.