An Impartial Bayesian Hypothesis Test for Audit Sampling

Auditors who perform audit sampling are often interested in obtaining evidence for or against the hypothesis that the misstatement in a population of items is lower than a critical limit, the so-called performance materiality. Here, we propose to perform this hypothesis test using a Bayesian approach that involves the use of an impartial prior distribution, assigning equal prior probabilities to the competing interval hypotheses. Firstly, we argue that the impartial prior distribution is sensible for auditors because it is easy to justify, interpret, and explain. Secondly, we show that Bayes factors computed using this prior distribution have desirable statistical properties. Finally, we compare these Bayes factors with traditional p-values in an audit sampling context and elaborate on the merits of the impartial Bayesian hypothesis test.