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On Sample Size of the Kruskal–Wallis Test with Application to a Mouse Peritoneal Cavity Study

Authors

  • Chunpeng Fan,

    Corresponding author
    1. Department of Biostatistics and Programming, sanofi-aventis BX2-416A, 200 Crossing Boulevard, P.O. Box 6890, Bridgewater, New Jersey 08807-0890, U.S.A.
      email: Chunpeng.Fan@sanofi-aventis.com
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  • Donghui Zhang,

    1. Department of Biostatistics and Programming, sanofi-aventis BX2-416A, 200 Crossing Boulevard, P.O. Box 6890, Bridgewater, New Jersey 08807-0890, U.S.A.
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  • Cun-Hui Zhang

    1. Department of Statistics and Biostatistics, Rutgers University, 504 Hill Center, Busch Campus, Piscataway, New Jersey 08854-8019, U.S.A.
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email: Chunpeng.Fan@sanofi-aventis.com

Abstract

Summary As the nonparametric generalization of the one-way analysis of variance model, the Kruskal–Wallis test applies when the goal is to test the difference between multiple samples and the underlying population distributions are nonnormal or unknown. Although the Kruskal–Wallis test has been widely used for data analysis, power and sample size methods for this test have been investigated to a much lesser extent. This article proposes new power and sample size calculation methods for the Kruskal–Wallis test based on the pilot study in either a completely nonparametric model or a semiparametric location model. No assumption is made on the shape of the underlying population distributions. Simulation results show that, in terms of sample size calculation for the Kruskal–Wallis test, the proposed methods are more reliable and preferable to some more traditional methods. A mouse peritoneal cavity study is used to demonstrate the application of the methods.

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