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Distributional properties for the generalized p-value for the Behrens-Fisher problem

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  • Tang, Shijie
  • Tsui, Kam-Wah

Abstract

The generalized p-value method introduced by Tsui and Weerahandi [1989. Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters. J. Amer. Statist. Assoc. 84 (406), 602-607] has been successfully used to provide small sample solutions for many hypothesis testing problems when nuisance parameters are present. Simulation studies show that generalized p-values have similar distributional properties as ordinary p-values. It is desirable to study theoretical properties of generalized p-values. Given a sample d, let p(d) be the generalized p-value for the Behrens-Fisher problem of testing the difference of two independent normal distribution means with possibly unequal distributional variances, as given in Tsui and Weerahandi [1989. Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters. J. Amer. Statist. Assoc. 84 (406), 602-607]. We derive a closed form expression to show that, for small samples, the probability P(p(d)[less-than-or-equals, slant]r) is approximately less than or equal to r, for 0[less-than-or-equals, slant]r[less-than-or-equals, slant]0.5.

Suggested Citation

  • Tang, Shijie & Tsui, Kam-Wah, 2007. "Distributional properties for the generalized p-value for the Behrens-Fisher problem," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 1-8, January.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:1:p:1-8
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    References listed on IDEAS

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    1. Gamage, Jinadasa & Mathew, Thomas & Weerahandi, Samaradasa, 2004. "Generalized p-values and generalized confidence regions for the multivariate Behrens-Fisher problem and MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 177-189, January.
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    1. Tsui, Kam-Wah & Tang, Shijie, 2007. "Simultaneous testing of multiple hypotheses using generalized p-values," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1362-1370, July.

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