A Statistical Paradox in Auditing

The decision rule in a standard form of hypothesis testing in auditing is to reject the null hypothesis (and thus the auditee's account balance) if the 100(1‐β)% confidence interval estimate of the population average error lies even partly outside the null (immaterial) interval. The effect of this rule is to fix the minimum power of the test (i.e., the minimum probability of rejecting a materially incorrect balance) at 1‐β/2 (assuming a two‐sided test). An unseen theoretical deficiency of the stated decision rule is that, from a Bayesian (evidential) rather than long‐run error‐frequency standpoint, marginal rejection of the null hypothesis supports that hypothesis. Indeed if the sample size is large enough, an account balance which is marginally rejected by the auditor, using a conventional test, has an‘objective’ (independent‐of‐prior) posterior probability arbitrarily close to one. In these circumstances, any call by the auditor for adjustment of the stated account balance, or additional sampling, would be seen as‘over‐servicing’ and rightfully resisted.