Bayesian equivalence testing for binomial random variables

Abstract

The equivalence testing problem is examined utilizing a Bayesian approach using Bayes factors. In this problem, it is desired to determine whether or not there exists evidence that two treatments exhibit little difference in their effectiveness. Barker et al. [Barker, L., Rolka, H., Rolka, D. and Brown, C., 2001, Equivalence testing for binomial random variables: which test to use? The American Statistician, 55, 279–287.] give a thorough discussion of the various classical two one-sided tests (TOSTs) that have been proposed for this problem along with two of their own. Bayesian alternatives to these tests are considered utilizing two different noninformative priors and an informative conjugate prior for the two population proportions. The noninformative Bayesian approaches appear to be attractive alternatives to these TOST procedures in certain situations with respect to power.

Keywords:

• Bayes factor
• Equivalence testing
• Noninformative prior
• Posterior distribution

Acknowledgements

The author wishes to thank Dr Sung C. Choi for his helpful comments.

Additional information

Notes on contributors

Patricia Pepple Williamson

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