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Default “Gunel and Dickey” Bayes factors for contingency tables

Authors
  • Jamil, Tahira1
  • Ly, Alexander1
  • Morey, Richard D.2
  • Love, Jonathon1
  • Marsman, Maarten1
  • Wagenmakers, Eric-Jan1
  • 1 University of Amsterdam, Department of Psychology, Nieuwe Prinsengracht 129B, Amsterdam, VZ, 1018, Netherlands , Amsterdam (Netherlands)
  • 2 Cardiff University, School of Psychology, Cardiff, UK , Cardiff (United Kingdom)
Type
Published Article
Journal
Behavior Research Methods
Publisher
Springer - Psychonomic Society
Publication Date
Jun 20, 2016
Volume
49
Issue
2
Pages
638–652
Identifiers
DOI: 10.3758/s13428-016-0739-8
Source
Springer Nature
Keywords
License
Green

Abstract

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).

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