A comparison of tests for restricted orderings in thethree-class case

Abstract

A variety of methods for comparing three distributions have been proposed in the literature. These methodsassess the same null hypothesis of equal distributions but differ in the alternative hypothesis they consider.The alternative hypothesis can be that measurements from the three classes are distributed according tounequal distributions or that measurements between the three classes follow a specific monotone ordering,an inverse-U-shaped (umbrella) ordering, or a U-shaped (tree) ordering. This paper compares these testswith respect to power and test size under different simulation scenarios. In addition, the methods areillustrated in two applications generated by different research questions with data from three classessuggesting monotone and umbrella orders. Additionally, proposals for the appropriate application of thesetests are provided. Copyrightq2009 John Wiley & Sons, Ltd.