The Use of Program BAYAUD in the Teaching of Audit Sampling

Abstract

" Statistical sampling is taught in Auditing classes at most academic institutions, but most CPA’s with whom we have talked have little understanding of the sampling process. This paper discusses the use of Bayesian statistics in the determination of the sample size, which is not in itself novel. However, the interactive program BAYAUD and the Big SAC Case, which was written to go with it, are somewhat novel. Classical sampling techniques have dominated the content of most discussions of sampling in auditing. The classical approach relies on the standard error formula, which requires that the variance of the population (or the sample proportion) be estimated in order to compute the sample size. This requirement becomes a major criticism, for most students and businessmen consider it counterintuitive that one must assume what the results of the audit will be in order to develop a sample design to provide these results. Another weakness of the classical approach is that it fails to consider explicitly the tradeoff between the accuracy of the added information and the cost of obtaining that information. The Bayesian approach to sample size determination is at least as subjective, if not more so, than the classical approach. However, it makes this subjectivity explicit and provides more basis for the discussion of how likely events are, and what action to take after the information has been assembled. Proponents of the use of Bayesian statistics in auditing have been numerous. It has been argued that the auditor should formally incorporate his impression of a firm’s internal control, gained from his past experience, with the sample information accumulated during the audit in order to get his best opinion of the current status of the firm. Further, several authors (Kraft, 1968; Smith, 1972; Sorenson, 1969; Tracy, 1969) stated that the amount of sample evidence needed should depend on the auditor’s past experience with the firm. Much of the literature on the Bayesian approach has viewed the auditing problem as one with discrete states of nature, i.e., there are only a finite number of error rates possible. For example, error rates of .001, .01, .05, and .10 may be hypothesized and the auditor assesses the prior probabilities of these rates. Likelihood probabilities are calculated from the sample data, as Bernouilli sampling is assumed; in general, the likelihood would be the probability of finding r errors given a "