Wild bootstrapping rank-based procedures: Multiple testing in nonparametric factorial repeated measures designs

Abstract

Repeated measures designs are frequently used for planning experiments in the life or social sciences. Typical examples include the comparison of different treatments over time, where both factor levels may possess an additional structure. For such designs, the statistical analysis typically consists of several steps. If the global null is rejected, multiple comparisons are performed. Usually, general factorial repeated measures designs are inferred by classical linear mixed models. Common underlying assumptions, such as normality or variance homogeneity are, however, often not met in practice. Furthermore, when dealing with, e.g., ordinal or ordered categorical data, means are no longer meaningful to describe an effect and other effect sizes should be used. To this end, we developmultiple contrast tests for nonparametric treatment effects in general factorial repeated measures designs within this paper and equip them with a novel, asymptotically correct wild bootstrap approach. Because regulatory authorities require the calculation of confidence intervals, this work also provides simultaneous confidence intervals for linear contrasts and for the ratio of different contrasts in meaningful effects. Extensive simulations are conducted to foster the theoretical findings. Finally, the analysis of two datasets exemplify the applicability of the novel procedures.