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, 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 ).
Department of Psychology, University of Amsterdam, Nieuwe Prinsengracht 129B, 1018, VZ, Amsterdam, Netherlands.
Tahira
T
Jamil
Department of Psychology, University of Amsterdam, Nieuwe Prinsengracht 129B, 1018, VZ, Amsterdam, Netherlands.
Alexander
A
Ly
School of Psychology, Cardiff University, Cardiff, UK.
Richard D
RD
Morey
Department of Psychology, University of Amsterdam, Nieuwe Prinsengracht 129B, 1018, VZ, Amsterdam, Netherlands.
Jonathon
J
Love
Department of Psychology, University of Amsterdam, Nieuwe Prinsengracht 129B, 1018, VZ, Amsterdam, Netherlands.
Maarten
M
Marsman
Department of Psychology, University of Amsterdam, Nieuwe Prinsengracht 129B, 1018, VZ, Amsterdam, Netherlands. ej.wagenmakers@gmail.com.
Eric-Jan
EJ
Wagenmakers
D001499:Bayes Theorem; D005163:Factor Analysis, Statistical; D006801:Humans; D012984:Software
Bayes factors; Contingency table; Sampling models; p-value