Comparative Classical and Bayesian Interpretations of Statistical Compliance Tests in Auditing

Within the theory of statistics there are three main schools. The two longest established are based on the works of Fisher and of Neyman and Pearson, these often being loosely grouped together under the heading ‘classical’ statistics. The third and oldest in terms of historical development rather than broad acceptance is the school of ‘non-classical’ or, more precisely, Bayesian statistics. The philosophical and methodological structures of these three distinct brands of statistical thinking have some points of intersection but ultimately differ from one another irreconcilably. In practical terms, this divergence leads to incompatible and, in some cases, diametrically opposite inferential outcomes, at the level of substance and not merely form, all on the same data. In auditing, such inconsistencies can be shown, for example, in the case of a standard statistical compliance test (attribute sampling) of the test prescribed in nearly all audit sampling textbooks. From the outset, auditors have interpreted this kind of test in the way proposed and popularised by Neyman and Pearson. On comparing the Neyman-Pearson standpoint with its Fisherian and Bayesian alternatives, only the Bayesian view is seen to withstand logical criticism.