Increasing Efficiency in Stratified Audit Sampling via Bayesian Hierarchical Modelling

Stratification is a statistical technique commonly used in audit sampling to increase efficiency. The reason for this increase is that stratification enhances the representativeness of the sample data and increases the accuracy of the misstatement estimate, which leads to a reduction in overall sample size. However, currently dominant methods for evaluating stratified audit samples have suboptimal efficiency. That is because these methods exclusively focus on the differences between the strata and do not acknowledge their similarities. In practice, this means that auditors often test more samples than necessary to reduce the audit risk to an appropriately low level. In this article, we propose an intuitive and powerful statistical approach to evaluate stratified audit samples that uses this information: Bayesian hierarchical modelling. We show that, compared to current methods, Bayesian hierarchical modelling consistently increases efficiency across many stratified audit sampling situations by reducing sample sizes by 63% up to 93%.