A Note on Optimal Sample Sizes in Compliance Tests Using a Formal Bayesian Decision-Theoretic Approach for Finite and Infinite Populations

Abstract

Recently, Godfrey and Andrews [1982], hereafter GA, compared sample size requirements in auditing using finite versus infinite Bayesian population models. They concluded that required sample sizes for finite population models would never be larger than those required for an infinite population, and that both Bayesian models require smaller sample sizes than classical procedures. However, neither GA nor prior researchers who have utilized informal Bayesian techniques (e.g., Felix and Grimlund [1977]) included possible loss functions in their analyses. Obviously, some loss function, whether stated explicitly or relied upon implicitly, must enter auditors' sample size determinations. In this paper we examine optimal sample sizes using a formal Bayesian decision-theoretic approach, in which auditors seek to maximize expected utility subject to a budgetary constraint. The results are presented for finite and infinite population models based on a linear loss function and the prior distribution mean error rates for audit populations taken from