Undominated p-Values and Property C for Unconditional One-Sided Two-Sample Binomial Tests
✍ Scribed by H. Frick
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 131 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0323-3847
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✦ Synopsis
In a recent paper Ro È hmel and Mansmann (1999) discussed p-values for unconditional two-sample binomial tests of the one-sided type. Since uniformly smallest p-values do not exist, they considered undominated or, in their notation, acceptable p-values. Ro Èhmel and Mansmann showed that any pvalue is dominated by a p-value induced by an appropriate statistic. For investigating acceptable pvalues it is therefore sufficient to consider the set of statistics. In this paper necessary and sufficient conditions and construction methods for statistics inducing acceptable p-values are discussed. The concept of property C of Barnard (1947) is examined in this context. For the classical null-hypothesis p 2 p 1 it turns out that property C and acceptability are mutually exclusive criteria. In order to reconcile both ideas, C-acceptable p-values are introduced, i.e. p-values which are undominated in the set of all p-values with property C. Barnard's celebrated unconditional test is shown to be of this type. A necessary and sufficient condition for statistics to induce C-acceptable p-values for the classical nullhypothesesis is formulated. Furthermore some numerical consequences of property C are discussed. Finally the p-value p R induced by Ro Èhmel and Mansmann's recently developed statistic is investigated. It is proven that p R is C-acceptable for all null-hypotheses.