JSM 2004 - Toronto

Abstract #300644

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Activity Number: 414
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract - #300644
Title: Bayesian Alternatives to "Exact" P Values in Sparse Two-way Tables
Author(s): Murray Aitkin*+ and Magreth Njau
Companies: University of Newcastle-upon-Tyne and University of Newcastle-upon-Tyne
Address: , Newcastle-upon-Tyne , International, NE1 7RU, United Kingdom
Keywords: two-way tables ; exact p value ; Bayes analysis ; Bayesian p value ; likelihood ratio ; likelihood ratio test
Abstract:

"Exact" (conditional) p values are widely used to assess the null hypothesis of independence or treatment homogeneity in sparse two-way contingency tables, where the likelihood ratio test (LRT) may fail to have its asymptotic chi-squared distribution. The "exact" p values are based on the conditional likelihood, taking the second margin of the table as fixed. The second term in the likelihood is ignored. This paper proposes Bayesian alternatives that use the full likelihood and are therefor efficient, with Dirichlet priors on the group multinomial probabilities. A result of Dempster (1974, 1997) extended by Aitkin (1997) is used to provide Bayesian alternatives to the p value; these alternatives also provide an assessment of the validity of the LRT p value. The power of the Bayesian procedure compared to the conditional procedure is assessed by simulation for some simple cases.

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