Generalizations of the Tests by Kruskal-Wallis, Friedman and van der Waerden for Split-plot Designs

Abstract

Generalizations of the 1-factorial tests by Kruskal-Wallis and Friedman, as well as of the van der Waerden test are proposed for factorial split-plot designs, both allowing interactions. They are compared in regard to the type I error control and the power with the parametric F test, including the Huynh-Feldt adjustment, the inverse normal transform (INT), the ANOVA type statistic by Brunner et al. (ATS), the aligned rank transform (ART), the L statistic by Puri \& Sen and a procedure by Koch. The two methods proposed show a perfect type I error control, except for two situations, and an attractive power, particularly in case of nonnormal distributions. The charm and advantage of these procedures are the possibility to apply them with statistical standard tools using only variable transformations and data management, and to receive results from well-known methods which are easy to understand.