Default "Gunel and Dickey" Bayes factors for contingency tables

Behav Res Methods. 2017 Apr;49(2):638-652. doi: 10.3758/s13428-016-0739-8.


The analysis of R×C contingency tables usually features a test for independence between row and column counts. Throughout the social sciences, the adequacy of the independence hypothesis is generally evaluated by the outcome of a classical p-value null-hypothesis significance test. Unfortunately, however, the classical p-value comes with a number of well-documented drawbacks. Here we outline an alternative, Bayes factor method to quantify the evidence for and against the hypothesis of independence in R×C contingency tables. First we describe different sampling models for contingency tables and provide the corresponding default Bayes factors as originally developed by Gunel and Dickey (Biometrika, 61(3):545-557 (1974)). We then illustrate the properties and advantages of a Bayes factor analysis of contingency tables through simulations and practical examples. Computer code is available online and has been incorporated in the "BayesFactor" R package and the JASP program ( ).

Keywords: Bayes factors; Contingency table; Sampling models; p-value.

MeSH terms

  • Bayes Theorem
  • Factor Analysis, Statistical*
  • Humans
  • Software*