Abstract
One-sided Bayes factors are obtained for the association in 2 by 2 tables, under three different sampling designs. These Bayes factors are relevant when one has a prior believe about the direction of an association. It is further shown how prior knowledge can be incorporated in determining the support of a positive association against the hypothesis of row-column independence.
Similar content being viewed by others
References
CLARK, K.B., and CLARK, M.P. (1947), “Racial Identification and Preference Among Negro Children”, in Readings in Social Psychology, ed. E.L. Hartley, New York: Holt, Rinehart, and Winston.
COOK, J.D. (2003), “Numerical Computation of Stochastic Inequality Probabilities”,MDACC Technical Report UTMDABTR-008-03, https://www.johndcook.com.
COOK, J.D. (2005), “Exact Calculation of Beta Inequalities”, MDACC technical report UTMDABTR-005-05, https://www.johndcook.com.
GUNEL, E., and DICKEY, J. (1974), “Bayes Factors for Independence in Contingency Tables”, Biometrika, 61, 545–557.
HRABA, J., and GRANT, G. (1970), “Black Is Beautiful: A Re-examination of Racial Preference and Identification”, Journal of Personality and Social Psychology, 16, 398.
JASP TEAM (2016), JASP (Version 0.7.5.5), Computer Software, https://jasp-stats.org/.
JAMIL, T., LY, A.,MOREY, R.D., LOVE, J.,MARSMAN, M., and WAGENMAKERS, E.-J. (2016), “Default “Gunel and Dickey” Bayes Factors for Contingency Tables”, Behavior Research Methods, http://link.springer.com/article/10.3758/s13428-016-0739-8.
KLUGKIST, I., and HOIJTINK, H. (2007), “The Bayes Factor for Inequality and About Equality ConstrainedModels”, Computational Statistics and Data Analysis, 51, 6367–6379.
LAVINE, M., and SCHERVISH, M.J. (1999), “Bayes Factors: What They Are and What They Are Not”, The American Statistician, 53, 119–122.
LUNN, D., SPIEGELHALTER, D., THOMAS, A., and BEST, N. (2009), “The BUGS Project: Evolution, Critique, and Future Directions”, Statistics in Medicine, 28, 3049–3067.
MOREY, R.D., and ROUDER, J.N. (2015), “BayesFactor: Computation of Bayes Factors for Common Designs. R package Version 0.9. 10-1, Computer Software Manual, http://CRAN.R-project.org/.
MOREY, R.D., and WAGENMAKERS, E.-J. (2014), “Simple Relation Between Bayesian Order-Restricted and Point-Null Hypothesis Tests”, Statistics and Probability Letters, 92, 121–124.
PLUMMER, M. (2003), “JAGS: A Program for Analysis of Bayesian Graphical Models Using Gibbs Sampling”, in Proceedings of the 3rd International Workshop on Distributed Statistical Computing, eds. K. Hornik, F. Leisch, and A. Zeileis, Vienna, Austria.
R CORE TEAM (2015), “R: A Language and Environment for Statistical Computing”, Vienna, Austria: R Foundation for Statistical Computing, https://www.R-project.org/.
SPRINGER, M.D., and THOMPSON, W.E. (1970), “The Distribution of Products of Beta, Gamma and Gaussian Random Variables”, SIAM Journal on Applied Mathematics, 18, 721–737.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ligtvoet, R. Exact One-Sided Bayes Factors for 2 by 2 Contingency Tables. J Classif 34, 465–472 (2017). https://doi.org/10.1007/s00357-017-9244-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00357-017-9244-8