Default “Gunel and Dickey” Bayes factors for contingency tables

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,...

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Bibliographic Details
Published in:Behavior research methods 2017-04, Vol.49 (2), p.638-652
Main Authors: Jamil, Tahira, Ly, Alexander, Morey, Richard D., Love, Jonathon, Marsman, Maarten, Wagenmakers, Eric-Jan
Format: Article
Language:English
Subjects:
Bayes Theorem
Bayesian analysis
Behavioral Science and Psychology
Cognitive Psychology
Computer simulation
Contingencies
Contingency
Contingency tables
Factor analysis
Factor Analysis, Statistical
Humans
Psychology
Sampling
Social sciences
Software
Tables
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Summary: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 ( jasp-stats.org ).
ISSN:1554-3528
1554-351X
1554-3528
DOI:10.3758/s13428-016-0739-8