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

Shijie Tang and Kam-Wah Tsui

Statistics & Probability Letters, 2007, vol. 77, issue 1, 1-8

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.

Keywords: Generalized; p-value; Behrens-Fisher; problem; Actual; size; of; a; test; Repeated; sampling; performance (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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