Undominatedp-Values and PropertyC for Unconditional One-Sided Two-Sample Binomial Tests
2000; Wiley; Volume: 42; Issue: 6 Linguagem: Inglês
10.1002/1521-4036(200010)42
ISSN1521-4036
Autores Tópico(s)Optimal Experimental Design Methods
ResumoIn a recent paper Röhmel 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. Röhmel and Mansmann showed that any p-value is dominated by a p-value induced by an appropriate statistic. For investigating acceptable p-values 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 p2 ≤ p1 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 null-hypothesesis is formulated. Furthermore some numerical consequences of property C are discussed. Finally the p-value πR induced by Röhmel and Mansmann's recently developed statistic is investigated. It is proven that πR is C-acceptable for all null-hypotheses.
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