Default “Gunel and Dickey” Bayes factors for contingency tables

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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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Bayesian Versus Orthodox Statistics: Which Side Are You On?

Zoltan Dienes (2011)

Researchers are often confused about what can be inferred from significance tests. One problem occurs when people apply Bayesian intuitions to significance testing-two approaches that must be firmly separated. This article presents some common situations in which the approaches come to different conclusions; you can see where your intuitions initially lie. The situations include multiple testing, deciding when to stop running participants, and when a theory was thought of relative to finding out results. The interpretation of nonsignificant results has also been persistently problematic in a way that Bayesian inference can clarify. The Bayesian and orthodox approaches are placed in the context of different notions of rationality, and I accuse myself and others as having been irrational in the way we have been using statistics on a key notion of rationality. The reader is shown how to apply Bayesian inference in practice, using free online software, to allow more coherent inferences from data.

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Bayesian hypothesis testing for psychologists: a tutorial on the Savage-Dickey method.

Eric-Jan Wagenmakers, Tom Lodewyckx, Himanshu Kuriyal … (2010)

In the field of cognitive psychology, the p-value hypothesis test has established a stranglehold on statistical reporting. This is unfortunate, as the p-value provides at best a rough estimate of the evidence that the data provide for the presence of an experimental effect. An alternative and arguably more appropriate measure of evidence is conveyed by a Bayesian hypothesis test, which prefers the model with the highest average likelihood. One of the main problems with this Bayesian hypothesis test, however, is that it often requires relatively sophisticated numerical methods for its computation. Here we draw attention to the Savage-Dickey density ratio method, a method that can be used to compute the result of a Bayesian hypothesis test for nested models and under certain plausible restrictions on the parameter priors. Practical examples demonstrate the method's validity, generality, and flexibility. Copyright 2009 Elsevier Inc. All rights reserved.

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Author and article information

Contributors

Eric-Jan Wagenmakers: ej.wagenmakers@gmail.com

Journal

Journal ID (nlm-ta): Behav Res Methods

Journal ID (iso-abbrev): Behav Res Methods

Title: Behavior Research Methods

Publisher: Springer US (New York )

ISSN (Print): 1554-351X

ISSN (Electronic): 1554-3528

Publication date (Electronic): 20 June 2016

Publication date PMC-release: 20 June 2016

Publication date (Print): 2017

Volume: 49

Issue: 2

Pages: 638-652

Affiliations

[1 ]ISNI 0000000084992262, GRID grid.7177.6, Department of Psychology, , University of Amsterdam, ; Nieuwe Prinsengracht 129B, 1018 VZ Amsterdam, Netherlands

[2 ]ISNI 0000 0001 0807 5670, GRID grid.5600.3, School of Psychology, , Cardiff University, ; Cardiff, UK

Article

Publisher ID: 739

DOI: 10.3758/s13428-016-0739-8

PMC ID: 5405059

PubMed ID: 27325166

SO-VID: bc8fb16c-a81d-4f8c-a7c2-d598c8720b7b

License:

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.