A wild bootstrap approach for nonparametric repeated measurements

Abstract

Repeated measures and split plot plans are often the preferred design of choice when planning experiments in life and social sciences. They are typically analyzed by mean-based methods from MANOVA or linear mixed models, requiring certain assumptions on the underlying parametric distribution. However, if count, ordinal or score data are present, these techniques show their limits since means are no adequate measure of deviations between groups. Here, nonparametric rank-based methods are preferred for making statistical inference. The common nonparametric procedures such as the Wald- or ANOVA-type tests, however, have drawbacks since they usually require large sample sizes for accurate test decisions. The aim is to enhance the small sample properties of these test statistics by means of a specific nonparametric bootstrap procedure while preserving their general applicability for all kinds of data in factorial repeated measures and split plot designs. In particular, it is shown that a specific wild bootstrap procedure inherits the large sample properties of the Wald- and ANOVA-type statistics while considerably improving their small sample behavior. The new method is motivated by and applied to a practical data example in a repeated measures design with score data.