STATISTICALLY INCOHERENT HYPOTHESIS TESTS IN AUDITING

Statistical hypothesis,tests in auditing assume the classical framework developed by Neyman and Pearson in the 1930s. In variables sampling, for example, the auditor tests the statistical hypothesis that an account balance is not materially misstated against its logical complement (material error), and, according to a predesignated decision rule with mathematically determinate error characteristics (alpha, beta), that hypothesis is either ''accepted'' or ''rejected.'' The problem which arises at this point, and which is not adequately treated in orthodox textbooks, either in auditing or in statistics itself, is that of how to interpret such test results in terms of evidence for or against the hypothesis tested. This paper examines the evidential content of results of classical hypothesis tests from the viewpoint of Bayesian statistics. A familiar test example is considered, and hypothetical data, which, on a classical view, marginally reject the auditee's stated account balance, are reinterpreted 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, the more so the larger the sample size. These findings support the longstanding argument that statistical inference in auditing would be both more reliable and more efficient if rooted in Bayesian rather than classical statistics.