Assessing Robustness of Intrinsic Tests of Independence in Two-Way Contingency Tables
نویسندگان
چکیده
A condition needed for testing nested hypotheses from a Bayesian viewpoint is that the prior for the alternative model concentrates mass around the smaller, or null, model. For testing independence in contingency tables, the intrinsic priors satisfy this requirement. Further, the degree of concentration of the priors is controlled by a discrete parameter m, the training sample size, which plays an important role in the resulting answer. In this paper we study, for small or moderate sample sizes, robustness of the tests of independence in contingency tables with respect to intrinsic priors with different degrees of concentration around the null. We compare these tests with frequentist tests and the robust Bayes tests of Good and Crook. For large sample sizes robustness is achieved since the intrinsic Bayesian tests are consistent. We also discuss conditioning issues and sampling schemes, and argue that conditioning should be on either one margin or the table total, but not on both margins. Examples using real are simulated data are given.
منابع مشابه
Intrinsic Tests of Independence in Contingency Tables
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