What question did this study set out to answer?

To explore the Bayes factors for independence in two-way contingency tables and their implications.

January 1, 1974

Bayes factors for independence in contingency tables

EGErdoǵan GünelWest Virginia University JDJames DickeyAugusta University

Key Points

To explore the Bayes factors for independence in two-way contingency tables and their implications.
Examined four standard statistical sampling models related by nested conditioning.
Derived conditions allowing prior distributions to induce corresponding distributions in further conditioned models.
Presented a theorem for factorized Bayes factors using a factorized likelihood function.
Demonstrated that Bayes factors can factorize, revealing evidence in marginal rows and columns.
Established bounds on marginal Bayes factors that support Fisher's conditioning practice.
Provided theoretical insights into the relationship between the prior distributions and evidence in contingency tables.

Abstract

The null hypothesis of row-column independence in a two-way contingency table can be expressed as a constraint on the parameters in various standard statistical sampling models. Four sampling models are considered, which are related by nested conditioning. By having the prior distribution in any one model induce the prior distribution in each further conditioned model, it is shown that the Bayes factors for independence will factorize, and there by expose the evidence residing in the marginal row and column of the table. Bounds on the marginal Bayes factors justify, in a weak sense, Fisher's practice of conditioning. A general theorem is given for factorized Bayes factors from a factorized likelihood function

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