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Optimal sample size planning for the Wilcoxon--Mann--Whitney and van Elteren tests under cost constraints

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  • Jiin-Huarng Guo

Abstract

Sampling cost is a crucial factor in sample size planning, particularly when the treatment group is more expensive than the control group. To either minimize the total cost or maximize the statistical power of the test, we used the distribution-free Wilcoxon--Mann--Whitney test for two independent samples and the van Elteren test for randomized block design, respectively. We then developed approximate sample size formulas when the distribution of data is abnormal and/or unknown. This study derived the optimal sample size allocation ratio for a given statistical power by considering the cost constraints, so that the resulting sample sizes could minimize either the total cost or the total sample size. Moreover, for a given total cost, the optimal sample size allocation is recommended to maximize the statistical power of the test. The proposed formula is not only innovative, but also quick and easy. We also applied real data from a clinical trial to illustrate how to choose the sample size for a randomized two-block design. For nonparametric methods, no existing commercial software for sample size planning has considered the cost factor, and therefore the proposed methods can provide important insights related to the impact of cost constraints.

Suggested Citation

  • Jiin-Huarng Guo, 2012. "Optimal sample size planning for the Wilcoxon--Mann--Whitney and van Elteren tests under cost constraints," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(10), pages 2153-2164, June.
  • Handle: RePEc:taf:japsta:v:39:y:2012:i:10:p:2153-2164
    DOI: 10.1080/02664763.2012.702265
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    References listed on IDEAS

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    1. Xiaofeng Liu, 2003. "Statistical Power and Optimum Sample Allocation Ratio for Treatment and Control Having Unequal Costs per Unit of Randomization," Journal of Educational and Behavioral Statistics, , vol. 28(3), pages 231-248, September.
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    Cited by:

    1. Doll, Monika & Klein, Ingo, 2018. "Sample size analysis for two-sample linear rank tests," FAU Discussion Papers in Economics 05/2018, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.

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