A Sampling Model for Audit Tests of Composite Accounts

A typical part of the public auditor's opinion formulation process is the evaluation of composite account balances resulting from the aggregation of a large number of subsidiary components. Numerous statistical methods have been proposed as a means of assisting the auditor in estimating the total value of such accounts or, equivalently, in estimating the error in the stated book value of such accounts. These methods, for the most part, are a direct adaptation of standard classical and Bayesian statistical procedures. Recent work by Kaplan [1973b] and Neter and Loebbecke [1975] has raised serious questions about the adequacy of applying many of these methods to the auditing environment. These difficulties arise when the auditor chooses to develop a statistical inference on the total error, based upon the relationship between book value and sample audit value of the subsidiary components of the account. Because of the usual low error rates experienced in such accounting populations, these auxiliary (ratio, regression, differences, etc.) estimators all suffer from a lack of normal distribution robustness of the sampling distribution. The problem is particularly apparent within the customary range of auditing sample sizes. In this paper, we present an alternative statistical sampling model that proceeds from a different perspective and, consequently, avoids some of the assumptions made by more conventional methods. Our analysis brings together, in a Bayesian framework, the book value, audit value, and informed judgment sources of evidence that can be used to evaluate a composite account. When a noninformative prior judgment