Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155276 | Statistics & Probability Letters | 2007 | 8 Pages |
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)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)⩽r)P(p(d)⩽r) is approximately less than or equal to r , for 0⩽r⩽0.50⩽r⩽0.5.