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

Authors

  • Todd A. Alonzo,

    Corresponding author
    1. Division of Biostatistics, University of Southern California, Keck School of Medicine 440 E. Huntington Dr, Suite 400, Arcadia, CA 91006, U.S.A.
    • Division of Biostatistics, University of Southern California, Keck School of Medicine 440 E. Huntington Dr, Suite 400, Arcadia, CA 91006, U.S.A.
    Search for more papers by this author
  • Christos T. Nakas,

    1. Laboratory of Biometry, School of Agricultural Sciences, University of Thessaly, Magnesia, Greece
    Search for more papers by this author
  • Constantin T. Yiannoutsos,

    1. Division of Biostatistics, Indiana University School of Medicine, Indianapolis, IN, U.S.A.
    Search for more papers by this author
  • Sherri Bucher

    1. Department of Pediatrics, Neonatal and Perinatal Medicine Section and IU-Kenya Program, Indiana University School of Medicine, Indianapolis, IN, U.S.A.
    Search for more papers by this author

Abstract

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. Copyright © 2009 John Wiley & Sons, Ltd.

Ancillary