Statistically incoherent hypothesis tests in auditing

A classical, Neyman-Pearson hypothesis test results in a decision (choice of action) justified not by any assessment of sample evidence, but by the pre-specified frequencies with which that procedure generates errors of the two possible types. By applying such a test in auditing, the hypothesis tested is accepted or rejected without the auditor having to consider whether the data observed confirms (in any degree), or disconfirms, that hypothesis. In contrast with the classical framework, the Bayesian approach is to evaluate the probability of the hypothesis tested conditional on the data observed, and then to make a decision on the basis of that revised probability. Decisions are thus evidence-based rather than rule-based. So as to compare the classical and Bayesian programs, a familiar test example is considered, and hypothetical data, which, on a classical view, marginally reject the auditee's stated account balance, are re-interpreted from a Bayesian, evidential perspective. The results of this comparison reveal that classical hypothesis tests in auditing do not have a consistent (from test-to-test) evidential basis, and, in Bayesian terms, are therefore "incoherent". Also, contrary to intuitive expectations, marginal rejection is found to imply evidence in favor of the auditee's stated balance. Asymptotically, an account balance which is rejected only marginally in a classical hypothesis test has an "objective" (not-dependent-on-prior) posterior probability arbitrarily close to one.