The equivalence of the mid p-value and the expected p-value for testing equality of two balanced Binomial proportions |
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| Institution: | 1. Graduate Institute of Statistics, National Central University, Chung-Li 32054, Taiwan;2. Department of Management Sciences and Decision Making, Tamkang University, Tamsui, Taipei county 251, Taiwan;3. Department of Mathematics, Malott Hall, Cornell University, Ithaca, NY 14853-4201, USA;1. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg, South Africa;2. Department of Statistical Sciences, University of Cape Town, Private Bag X3, Rondebosch 7701, South Africa;3. Office of the Vice-Chancellor, Strathmore University, Nairobi, Kenya;1. Centro de Estatística e Aplicações, Faculdade de Ciências, Universidade de Lisboa, Portugal;2. Centro de Estatística e Aplicações, Universidade de Lisboa, Portugal;3. Departamento de Matemática, Universidade dos Açores, Portugal;4. Centro de Matemática e Aplicações, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Portugal |
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| Abstract: | This paper considers the problem of testing equality between two independent binomial proportions. Hwang and Yang (Statist. Sinica 11 (2001) 807) apply the Neyman–Pearson fundamental lemma and the estimated truth approach to derive optimal procedures, named expected p-values. This p-value has been shown to be identical to the mid p-value in Lancaster (J. Amer. Statist. Assoc. (1961) 223) for the one-sided test. For the two-sided test, the paper proves the usual two-sided mid p-value is identical to the expected p-value in the balanced sample case. |
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