A comparison of tests for restricted orderings in the three-class case

Todd A. Alonzo, Christos T. Nakas, Constantin T. Yiannoutsos, Sherri Bucher

Research output: Contribution to journalArticle

13 Scopus citations


A variety of methods for comparing three distributions have been proposed in the literature. These methods assess 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 to unequal 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 tests with respect to power and test size under different simulation scenarios. In addition, the methods are illustrated in two applications generated by different research questions with data from three classes suggesting monotone and umbrella orders. Additionally, proposals for the appropriate application of these tests are provided.

Original languageEnglish (US)
Pages (from-to)1144-1158
Number of pages15
JournalStatistics in Medicine
Issue number7
StatePublished - Mar 30 2009


  • Area under ROC curve
  • Kruskal-Walis test
  • Non-parametric tests
  • Ordered alternatives
  • Umbrella alternatives
  • Umbrella ROC volume
  • Volume under the ROC surface
  • Wilcoxon-Mann-Whitney test

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability

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