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There has been strong recent interest in testing interval null hypothesis forimproved scientific inference. For example, Lakens et al (2018) and Lakens andHarms (2017) use this approach to study if there is a pre-specified meaningfultreatment effect in gerontology and clinical trials, which is different fromthe more traditional point null hypothesis that tests for any treatment effect.Two popular Bayesian approaches are available for interval null hypothesistesting. One is the standard Bayes factor and the other is the Region ofPractical Equivalence (ROPE) procedure championed by Kruschke and others overmany years. This paper establishes a formal connection between these twoapproaches with two benefits. First, it helps to better understand and improvethe ROPE procedure. Second, it leads to a simple and effective algorithm forcomputing Bayes factor in a wide range of problems using draws from posteriordistributions generated by standard Bayesian programs such as BUGS, JAGS andStan. The tedious and error-prone task of coding custom-made software specificfor Bayes factor is then avoided.

Connecting Bayes factor and the Region of Practical Equivalence (ROPE) Procedure for testing interval null hypothesis