A Condition to Obtain the Same Decision in the Homogeneity Testing Problem from the Frequentist and Bayesian Point of View |
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Authors: | Miguel A Gómez-Villegas Beatriz González-Pérez |
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Institution: | 1. Departamento de Estadística e Investigación Operativa I , Universidad Complutense de Madrid , Madrid , Spain ma.gv@mat.ucm.es;3. Departamento de Estadística e Investigación Operativa I , Universidad Complutense de Madrid , Madrid , Spain |
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Abstract: | We develop a Bayesian procedure for the homogeneity testing problem of r populations using r × s contingency tables. The posterior probability of the homogeneity null hypothesis is calculated using a mixed prior distribution. The methodology consists of choosing an appropriate value of π0 for the mass assigned to the null and spreading the remainder, 1 ? π0, over the alternative according to a density function. With this method, a theorem which shows when the same conclusion is reached from both frequentist and Bayesian points of view is obtained. A sufficient condition under which the p-value is less than a value α and the posterior probability is also less than 0.5 is provided. |
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Keywords: | Contingency tables p-values Posterior probabilities Reconciliation |
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