Bayesian regions of evidence (for normal distributions)

Bayesian data analysis allows a researcher to assess whether a claim about an effect (e.g. effect > 0, effect > Δ, |effect| < Δ)) is justified given the data and a prior distribution, expressing her or his personal belief before seeing the data. However, the recipients of the analysis might use different priors, so it remains unclear whether they would share the claim. "Reverse Bayes" analysis and the "sufficiently sceptical prior" address this problem by asking how strongly one may believe in the absence of an effect in order to be convinced otherwise by the data. A method called "Region of Evidence" is presented that takes this idea and extends it for any normal prior (and a normally distributed estimate). It visualises all the priors that, if they had been used, would support the claim, including those that favour a positive or negative effect. Since the method depends only on an estimate and its standard error, it can be easily applied to previously published results. The paper describes the method and its implementation in a new Stata command called arevi, which can be freely used and modified.