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Decision theory analysis of audit discovery sampling

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  • DAVID R. FINLEY

Abstract

. Discovery sampling is a frequently used auditing technique. The objective of discovery sampling is to decide whether to accept or reject an audit population for which acceptance is appropriate only if the occurrence rate of serious errors is very low. This objective is met by auditing a sample and accepting only if the sample is free of serious errors. This paper first develops a Bayesian decision theory approach to the discovery sampling problem. Using this approach the auditor optimizes sampling effort according to a decision model that explicitly includes such factors as risk of failure of accepting too high an error rate, losses from wrong decisions, sampling costs, and prior distribution of the error rate. The form of the loss function used includes both linear and quadratic loss functions as special cases. Methods and formulas applicable to various prior distributions for the error rate are obtained. Detailed results are derived for two state†prior and gamma†prior distributions. A minimax approach that removes the need to elicit a complete prior distribution is then developed. Explicit formulas are obtained for both the admissible sample size range and for the minimax sample size. A comparison of results indicates that the minimax approach is nearly as efficient as approaches that require elicitation of prior problem rate distributions. Further analysis generalizes the methods by showing that for the Bayesian and minimax methods, analytical results can be derived for various forms of loss functions. Résumé. Le sondage de dépistage est une technique fréquemment utilisée en vérification qui a pour objectif de déterminer s'il faut accepter ou rejeter une population pour laquelle l'acceptation n'est appropriée que si la fréquence d'erreurs graves est très faible. L'objectif est réalisé au moyen de la vérification d'un échantillon et de son acceptation seulement si l'échantillon est exempt d'erreurs graves. L'auteur met d'abord au point une méthode inspirée de la théorie bayesienne de la décision, adaptée au problème du sondage de dépistage. En utilisant cette méthode, le vérificateur optimise le travail d'échantillonnage conformément à un modèle de décision qui comprend explicitement des facteurs tels que le risque d'échec ou le risque d'acceptation d'un taux d'erreur trop élevé, les pertes attribuables à de mauvaises décisions, les coûts d'échantillonnage et la distribution a priori du taux d'erreur. Des formes de fonction de perte utilisées, celles linéaires et quadratiques constituent des cas spéciaux. L'auteur obtient des méthodes et des formules applicables aux diverses distributions a priori du taux d'erreur. Il dérive les résultats analytiques pour les distributions a priori binômiale et gamma. L'auteur met ensuite au point une méthode minimax supprimant la nécessité d'obtenir une distribution a priori complète. Il obtient des formules explicites pour la fourchette de tailles d'échantillons admissibles ainsi que pour la taille de l'échantillon minimax. Une comparaison des résultats indique que la méthode minimax est presque aussi efficace que les méthodes qui exigent l'obtention de distributions a priori de taux d'erreurs. Le prolongement de l'analyse permet de généraliser les méthodes; il démontre en effet que pour les méthodes bayesienne aussi bien que minimax, les résultats analytiques peuvent être dérivés pour diverses formes de fonctions de perte.

Suggested Citation

  • David R. Finley, 1989. "Decision theory analysis of audit discovery sampling," Contemporary Accounting Research, John Wiley & Sons, vol. 5(2), pages 692-719, March.
  • Handle: RePEc:wly:coacre:v:5:y:1989:i:2:p:692-719
    DOI: 10.1111/j.1911-3846.1989.tb00734.x
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    References listed on IDEAS

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    1. Teitlebaum, Ad & Robinson, Cf, 1975. "Real Risks In Audit Sampling," Journal of Accounting Research, Wiley Blackwell, vol. 13, pages 70-91.
    2. Kaplan, Rs, 1975. "Sample-Size Computations For Dollar-Unit Sampling," Journal of Accounting Research, Wiley Blackwell, vol. 13, pages 126-133.
    3. Kinney, Wr, 1975. "Decision-Theory Approach To Sampling Problem In Auditing," Journal of Accounting Research, Wiley Blackwell, vol. 13(1), pages 117-132.
    4. Menzefricke, U, 1983. "On Sampling Plan Selection With Dollar-Unit Sampling," Journal of Accounting Research, Wiley Blackwell, vol. 21(1), pages 96-105.
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    6. Menzefricke, U, 1984. "Using Decision-Theory For Planning Audit Sample-Size With Dollar Unit Sampling," Journal of Accounting Research, Wiley Blackwell, vol. 22(2), pages 570-587.
    7. Kinney, Wr, 1975. "Decision-Theory Aspects Of Internal Control-System Design-Compliance And Substantive Tests," Journal of Accounting Research, Wiley Blackwell, vol. 13, pages 14-29.
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