Wild Bootstrapping Rank-Based Procedures: Multiple Testing in Nonparametric Split-Plot Designs

TL;DR

This paper introduces a new wild bootstrap method for rank-based multiple testing in nonparametric split-plot designs, addressing issues of assumption violations and providing valid confidence intervals.

Contribution

It develops a novel wild bootstrap approach for multiple contrast tests and confidence intervals in nonparametric split-plot designs, applicable to ordinal and categorical data.

Findings

The proposed method performs well in simulations under various conditions.

It provides valid simultaneous confidence intervals for contrasts.

Application to real datasets demonstrates practical utility.

Abstract

Split-plot or 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 factors may possess an additional factorial structure. For such designs, the statistical analysis usually consists of several steps. If the global null is rejected, multiple comparisons are usually performed. Usually, general factorial repeated measures designs are inferred by classical linear mixed models. Common underlying assumptions, such as normality or variance homogeneity are often not met in real data. Furthermore, to deal even with, e.g., ordinal or ordered categorical data, adequate effect sizes should be used. Here, multiple contrast tests and simultaneous confidence intervals for general factorial split-plot designs are developed and equipped with a novel asymptotically correct wild bootstrap approach. Because the regulatory authorities typically require the calculation of confidence intervals, this work also provides simultaneous confidence intervals for single contrasts and for the ratio of different contrasts in meaningful effects. Extensive simulations are conducted to foster the theoretical findings. Finally, two different datasets exemplify the applicability of the novel procedure.