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A comparison of tests for restricted orderings in the three‐class case
Author(s) -
Alonzo Todd A.,
Nakas Christos T.,
Yiannoutsos Constantin T.,
Bucher Sherri
Publication year - 2009
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.3536
Subject(s) - monotone polygon , class (philosophy)
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.