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