Reviews the book "Practical Statistical Sampling for Auditors," by Arthur J. Wilburn.

Auditing, Sampling, Substantive test, James-Stein Estimator

[This paper takes a Bayesian approach to incorporate auditors' prior information in constructing error bounds for the proportion of dollar amount overstated (equivalently, the total amount overstated) in an accounting population. The multinomial distribution model within the dollar-unit sampling framework suggested by Fienberg, Neter, and Leitch [1977] is used, and the prior distribution belongs to the class of Dirichlet distributions. The properties of the resulting Bayesian bounds are discussed. Some comparisons of tightness of bounds are made with the multinomial and the modified multinomial bounds [Leitch, et al., 1982]. Simulation results suggest that some of the Bayesian bounds have good repeated sampling properties. In particular, in repeated sampling, a Bayesian bound gives a significance level close to the nominal level for many typical accounting populations. Another advantage of the suggested approach is computational efficiency which is independent of the sample size and the number of errors found in the sample.]

This paper takes a Bayesian approach to incorporate auditors' prior information in constructing error bounds for the proportion of dollar amount overstated (equivalently, the total amount overstated) in an accounting population. The multinomial distribution model within the dollar-unit sampling framework suggested by Fienberg, Neter, and Leitch [1977] is used, and the prior distribution belongs to the class of Dirichlet distributions. The properties of the resulting Bayesian bounds are discussed. Some comparisons of tightness of bounds are made with the multinomial and the modified multinomial bounds [Leitch, et al., 1982]. Simulation results suggest that some of the Bayesian bounds have good repeated sampling properties, in particular, in repeated sampling, a Bayesian bound gives a significance level close to the nominal level for many typical accounting populations. Another advantage of the suggested approach is computational efficiency which is independent of the sample size and the number of errors found in the sample.

This paper describes an extension of the Tsui, Matsumura, and Tsui (1985) procedure, which is based on a multinomial distribution model within the dollar‐unit sampling framework, with a Dirichlet prior distribution. The extended model and a different Dirichlet prior are used in this study to generate upper and lower bounds and two‐sided confidence intervals for situations in which both understatement and overstatement errors are possible. The reported simulation study indicates that the achieved confidence levels of the proposed estimates are usually close to or greater than the nominal levels in repeated sampling for the populations studied. Résumé. Les auteurs décrivent une extension du procédé de Tsui, Matsumura et Tsui (1985) basée sur un modèle de distribution multinômiale dans le contexte de l'échantillonnage en unités monétaires, avec une distribution a priori de Dirichlet. Les auteurs utilisent l'extension du modèle et une distribution a priori de Dirichlet différente pour obtenir des limites supérieures et inférieures, et des intervalles de confiance bilatéraux pour les cas où des erreurs de sous‐évaluation aussi bien que de surévaluation sont envisageables. L'étude de simulation qui fait l'objet du compte rendu montre que les niveaux de confiance obtenus relativement aux estimations proposées se rapprochent habituellement des valeurs nominales où les excèdent lorsqu'on procède à des échantillonnages répétés des populations à l'étude.