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On power and sample size computation for multiple testing procedures

Author

Listed:
  • Chen, Jie
  • Luo, Jianfeng
  • Liu, Kenneth
  • Mehrotra, Devan V.

Abstract

Power and sample size determination has been a challenging issue for multiple testing procedures, especially stepwise procedures, mainly because (1) there are several power definitions, (2) power calculation usually requires multivariate integration involving order statistics, and (3) expansion of these power expressions in terms of ordinary statistics, instead of order statistics, is generally a difficult task. Traditionally power and sample size calculations rely on either simulations or some recursive algorithm; neither is straightforward and computationally economic. In this paper we develop explicit formulas for minimal power and r-power of stepwise procedures as well as complete power of single-step procedures for exchangeable and non-exchangeable bivariate and trivariate test statistics. With the explicit power expressions, we were able to directly calculate the desired power, given sample size and correlation. Numerical examples are presented to illustrate the relationship among power, sample size and correlation.

Suggested Citation

  • Chen, Jie & Luo, Jianfeng & Liu, Kenneth & Mehrotra, Devan V., 2011. "On power and sample size computation for multiple testing procedures," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 110-122, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:110-122
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    References listed on IDEAS

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    1. Dunnett, Charles W. & Tamhane, Ajit C., 1993. "Power comparisons of some step-up multiple test procedures," Statistics & Probability Letters, Elsevier, vol. 16(1), pages 55-58, January.
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    Cited by:

    1. Li, Yang & Zhao, Hui & Sun, Jianguo & Kim, KyungMann, 2014. "Nonparametric tests for panel count data with unequal observation processes," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 103-111.
    2. He, Simin & Pan, Xintong, 2024. "Advice and behavior in a dictator game: An experimental study," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 111(C).

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