In conventional dollar unit sampling (DUS) the “alpha” risk of erroneously rejecting an acceptable accounting population generally can be held to reasonable levels by working with a sufficiently large audit sample. Kaplan (1975) has discussed how such a DUS sample size may be chosen when controlling both the alpha and beta risk. However, as illustrated in this paper, neither Kaplan's procedure nor other previously developed DUS procedures provide a workable method that effectively controls for both the alpha and beta risk with small sample sizes or with accounting populations that have comparable understatement and overstatement errors. This paper presents a hypothesis‐testing approach to DUS that provides a solution to this problem. “Power curves” based on a large number of simulation studies of the new approach are presented in order to illustrate the reliability of the approach. Comparisons are also made with the corresponding power curves for two Stringer‐based confidence bound methods of DUS. In these comparisons, the new hypothesis‐testing approach to DUS appears to provide more favorable audit performance with smaller sample sizes than do the conventional DUS methods, although the primary advantage of the approach lies in its ability to control for both effectiveness ( beta risk) and efficiency ( alpha risk). Résumé. Dans les méthodes traditionnelles de sondage des unités monétaires (SUM), le risque «alpha», soit le risque de rejeter à tort une population comptable acceptable, peut en général être maintenu à des niveaux raisonnables si l'on travaille avec un échantillon de vérification suffisamment grand. Kaplan (1975) a traité de la façon de choisir une taille d'échantillon suffisamment grande aux fins du SUM dans les cas où l'on contrôle à la fois le risque alpha et le risque bêta. Toutefois, comme le démontrent les auteurs, ni la méthode de Kaplan ni les autres méthodes de SUM mises au point précédemment n'offrent de technique simple permettant de contrôler efficacement le risque alpha en même temps que le risque bêta avec de petites tailles d'échantillon ou des populations comptables présentant des erreurs de sous‐estimation et de surestimation comparables. Les auteurs suggèrent une méthode de test d'hypothèse, relativement au SUM, qui résout ce problème. Ils présentent des «courbes de puissance», fondées sur un grand nombre de cas de simulation de la nouvelle méthode, dans le but d'en illustrer la fiabilité. Ils établissent également des comparaisons avec les courbes de puissance correspondantes pour deux méthodes de limite de confiance du SUM, fondées sur les travaux de Stringer. Dans ces comparaisons, les nouvelles méthodes de test d'hypothèse en ce qui a trait au SUM semblent offrir un meilleur rendement de vérification lorsque les tailles d'échantillon sont petites que les méthodes traditionnelles de SUM, bien que l'avantage primordial de la méthode réside dans le fait qu'elle permet de contrôler à la fois l'efficacité (risque bêta ) et l'efficience (risque alpha ).

Test results are presented on the relative performance of two new auditing procedures for dollar-unit sampling--the quasi-Bayesian method developed by McCray [1984] and a slightly modified version of the moment method developed by Dworin and Grimlund [1984]. Extensive simulation studies of 96 representative accounts receivable and inventory populations were conducted. Both methods were found to be reliable over the tested range, and both provided tighter confidence bounds than those provided by the Stringer bound. This is the first study that has been made of the reliability of the quasi-Bayesian bound and of the comparative performance of the quasi-Bayesian and the moment methods. The moment method provided a tighter confidence bound at low error rates. For populations with high error rates, for which the true mean error was either very nearly zero or very large, the quasi-Bayesian method provided a tighter bound. Both bounds provided comparable results for the remaining intermediate cases. While either can be successfully used in these cases, the moment method appears to be easier to implement on currently available personal computers.

[Test results are presented on the relative performance of two new auditing procedures for dollar-unit sampling-the quasi-Bayesian method developed by McCray [1984] and a slightly modified version of the moment method developed by Dworin and Grimlund [1984]. Extensive simulation studies of 96 representative accounts receivable and inventory populations were conducted. Both methods were found to be reliable over the tested range, and both provided tighter confidence bounds than those provided by the Stringer bound. This is the first study that has been made of the reliability of the quasi-Bayesian bound and of the comparative performance of the quasi-Bayesian and the moment methods. The moment method provided a tighter confidence bound at low error rates. For populations with high error rates, for which the true mean error was either very nearly zero or very large, the quasi-Bayesian method provided a tighter bound. Both bounds provided comparable results for the remaining intermediate cases. While either can be successfully used in these cases, the moment method appears to be easier to implement on currently available personal computers.]

A new method of statistical analysis for DUS is presented in this paper. This method is based on a three-moment representation of the sampling distribution for the mean error. The performance of the resulting upper confidence bound is examined in 236 separate simulation studies covering the error rates and tainting patterns observed in actual accounts receivable and inventory accounts. The bound is easily calculated and reliable. It would result in the correct acceptance of more accounts receivable populations than the multinomial bound when the materiality limit is less than four percent. It does a significantly better job of dealing with inventory populations with both overstatement and understatement errors than the currently available methods.

Reviews the book "Programmed Guide to Tax Research," by James E. Parker.