Models for Computing Upper Error Limits in Dollar-Unit Sampling

Abstract

Auditors frequently rely on statistical sampling procedures to verify the correctness of an account balance. One such procedure, dollar-unit sampling (DUS), has been specifically developed for use in the auditing environment where very low error rates in account balances are often encountered. A development of DUS, along with discussions of its particular advantages and shortcomings, can be found in Anderson and Teitlebaum [1973], Kaplan [1975], Meikle [1972], and Neter, Goodfellow, and Loebbecke [1973]. The purpose of this paper is to investigate how one aspect of the DUS procedure can be improved. In particular, I propose alternative methods of computing upper error limits on the book value of the account being audited once the DUS sample has been selected. Using the compound Poisson process to model the error rate and the distribution of error sizes in the population of dollars being audited, I show (through simulations) how rather crude models of this type can be effectively integrated with Bayesian procedures to compute much tighter upper error limits than those obtained by the usual DUS method. The specific models developed in this paper are intended to be examples of the types of models about which auditors should begin thinking. The analysis also illustrates the usefulness of prior information about the population being audited in making upper error limit statements about the population.