This paper presents a quasi-Bayesian model that generates a discrete posterior probability distribution on the expected total error in a population for any dollar unit sample and any given discrete or continuous prior probability distribution on the expected total error in a population. The model can be used with any sample size and any number of overstatements and understatements. In addition, it is the only dollar unit sampling evaluation procedure that can use data on the proportion of total dollars of each tainting found in the sample or known or assumed to exist in the population. Comparisons of the proposed and multinomial upper bounds are presented. These comparisons strongly suggest that the proposed model is a reasonable approach for evaluating dollar unit samples even if an informative prior probability distribution on the expected total error is not available.

The primary reason for writing the manuscript, "A Quasi-Bayesian Audit Risk Model for Dollar Unit Sampling" was to: (1) present a model which could provide auditors with a complete posterior probability distribution on the amount of error in an account instead of just a single measure of the ultimate risk like an upper bound and (2) compare the Quasi-Bayesian measure of ultimate risk with other measures of ultimate risk. The question of how well the different measures of ultimate risk are integrated into an overall audit approach is left for future research. The respondent's comments defend his firm's overall audit approach, but fail to address the audit risk formula, which his firm uses. The manuscript intended to question the validity of the audit risk formula rather than his firm's audit approach. The reason for comparing the Quasi-Bayesian audit risk model with the audit risk formula in statement on auditing standards was to demonstrate, from a Bayesian perspective, that the audit risk formula considered by itself can significantly understate the ultimate risk of failing to detect a material error.

The article informs that when a student is first introduced to the concepts of compound interest, the functional relationships between the different variables are often confusing. This author has been successful in introducing the concepts of the present value of an ordinary annuity by using: a formula approach, problems that relate directly to the individual, and a present value of an ordinary annuity table with at least 360 periods and interest rates expressed to facilitate compounding monthly. Several examples follow. Two points about the formula should be stressed. First, the formula contains four variables. If three are known, the fourth can easily be found algebraically. Second, since there are four variables (PVA, i,n, P), the formula can be used to solve four different types of problems.