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A bayesian test for a two‐way contingency table using independence priors
Author(s) -
Albert James H.
Publication year - 1990
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315841
Subject(s) - contingency table , mathematics , bayes factor , test statistic , prior probability , independence (probability theory) , statistic , statistics , bayes' theorem , bayesian probability , statistical hypothesis testing
One method of testing for independence in a two‐way table is based on the Bayes factor, the ratio of the likelihoods under the independence hypothesis H and the alternative hypothesis H. The main difficulty in this approach is the specification of prior distributions on the composite hypotheses H and H. A new Bayesian test statistic is constructed by using a prior distribution on H that is concentrated about the “independence surface” H. Approximations are proposed which simplify the computation of the test statistic. The values of the Bayes factor are compared with values of statistics proposed by Gunel and Dickey (1974), Good and Crook (1987), and Spiegelhalter and Smith (1982) for a number of two‐way tables. This investigation suggests a strong relationship between the new statistic and the p ‐value.