A Minimum‐cost Audit Sampling Methodology Under Conditions of Predetermined Beta Risk

Abstract. This paper systematically analyzes the factors that affect sampling risks of the two major classes of statistical estimators in auditing. It develops three approaches for identifying when a particular estimator is preferred ex ante. It also provides a simulation analysis of ex ante-ex post sampling nsk differences. The paper concludes that dollarunit sampling may be more widely used than previous research has indicated.Resume. Cet article analyse de fagon systematique les facteurs d'lnfluence du risque €chantillonnal attache aux deux grandes categories d'estimateurs statistiques en verification. Trois approches sont developpees afin d'identifier les circonstances ou un estimateur particulier s'avere preferable ex ante. Une analyse de simulation portant sur les differences de risque echantillonnal ex ante et ex post est egalement presentee. Cet article conclut que la methode d'echantillonnage en unites monetaires semble plus utilisee que ce que la recherche anterieure laisse entendre.

Section: Discussionmentioning

confidence: 99%

Control of sampling risks in auditing*

Smieliauskas

1986

“…Two types of models have heen used to manage the tradeoff between the objectives of effectiveness and efficiency and to improve the overall quality of audit planning decisions. They are decision theory (DT) models (e,g., Kinney, 1975;Scott, 1975;Menzefricke, 1984) and constrained optimization (CO) models (e.g., Boockholdt and Finley, 1980;Menzefricke, 1983), DT models determine audit planning decision outcomes that minimize total expected loss. Although Cushing and Loebbecke (1983) cite the promise of decision-theoretic approaches to improve audit judgment modeling, applications of this approach have been limited.…”

Section: Theoretical Basis and Prior Researchmentioning

confidence: 99%

A multiple criteria model for audit planning decisions*

Bedard

Gopi²,

Vijayalakshmi

1991

Abstract. The auditor must trade off potential losses from both ineffectiveness (failure to detect client errors) and inefficiency. However, auditing standards do not specify how the auditor is to achieve ati appropriate balance between these two conflicting objectives. This paper presents a multiple criteria decision-making (MCDM) model of an audit planning decision in which an effectiveness vs, efficiency trade-off is required. The key advantage of the MCDM model developed here is that an optimal solution is obtained without requiring ex ante .specification of a loss function by the auditor. Thus, the model addresses a previously recognized problem (e.g,, Menzefricke, 1984) that loss functions may vary depending on characteristics of the audit. In this paper, we develop a model of the auditor's sampling plan selection problem incorporating multiple decision criteria, use the model under a variety of simulated audit conditions, and compare our results with previous research.Resume. Le verificateur doit parvenir a un compromis entre les pertes pouvant etre occasionnees a la fois par Tinefficacite (non-detection d'erreurs commises par I'entreprise cliente) et Tinefficience, Les normes de verification ne precisem cependant pas comment le verificateur doit parvenir a un equilibre approprie entre ces deux objectifs conflictuels. Les auteurs proposent un modele de decision a criteres multiples qui s'applique a la decision de planification de la verification esigeant un compromis efficacite-efficience, Le principal avantage de ce modele est qu'il permet d'obtenir une solution optimaie sans exiger la formulation ex ante par le verificateur d'une fonction de perte, Le modele porte done sur une question sur laquelle se sonl deja penches les chercheurs (Menzefricke, 1984, par exemple) : les fonctions de perte peuvent varier selon les caracteristiques de la veritication. Les auteurs elaborent ici un modele qui s'applique au probleme de selection par le verificateur d'un plan d'echantillonnage incorporant des criteres de decision multiples, Ils utilisent le modele en simulant diverses situations de verification et comparent les resultats obtenus avec ceux des travaux precedents. IntroductionThe auditor must trade off potential losses from two sources: undetected client errors (which reduce effectiveness) and overauditing (which reduces efficiency),

“…There appears to be little or no research on sampling cost patterns for audit sampling. Hence, I will follow the obvious predominant assumption by making such costs variable with the sample size n (e.g., Kinney (1975aKinney ( , 1975b; Boockholdt and Finley (1980); Menzefricke (1983)).…”

Section: Detailed Specificationsmentioning

confidence: 99%

“…In practice and in some well-known audit sampling models, it is common to base formal sampling plan analyses only on two possibilities, one denoting the acceptable condition and the other the threshold unacceptable condition (Elliot and Rogers (1972); Kinney (1975aKinney ( , 1975b; Kaplan (1975); Boockholdt and Finley (1980); Menzefricke (1983); Roberts (1978)). Kinney (1975a, p. 118) refers to this as the two-state world assumption.…”

Section: Application To Two State Decision Modelmentioning

confidence: 99%

Decision theory analysis of audit discovery sampling*

Finley

1989

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 gammaprior 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. .\ 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.Resume. Le sondage de d6pistage est une technique fr6quemment utilisee en verification qui a pour objectif de d6terminer s'il faut accepter ou rejeter une population pwur laquelle l'acceptation n'est appropri6e que si la frequence d'erreurs graves est trhs faible. L'objectif est F6alis6 au moyen de la verification d'un 6chantillon et de son acceptation seulement si l'dchantillon est exempt d'erreurs graves. L'auteur met d'abord au point une mdthode inspirde de la th^orie bayesienne de la ddcision, adaptde au probldme du sondage de ddpistage. En utilisant cette m^thode, le vddficateur optimise le travail d'echantillonnage conformdment k un modMe de decision qui comprend explicitement des facteurs tels que le risque d'dchec ou le risque d'acceptation d'un taux d'erreur trop eleve, les pertes attribuables k de mauvaises decisions, les couts d'dchantillonnage et la distribution a priori du taux d'erreur. Des formes de fonction de perte utilis6es, celles Iin6aires et quadratiques constituent des cas sjj^ciaux. L'auteur obtient des m6thodes et des formules * The author wishes to thank Shane Moriarity for suggesting this project and Haim Falk for his suggestions and encouragement. The author especially wishes to thank an anonymous referee for timely reviews and many meritorious suggestions for improvement. Mialytiques pour les distributions a priori bindmiale et gamma. L'auteur met ensuite au point une m6thode minimax supprimant la n6cessit€ d'obtenir une distribution a priori complete. II obtient des formules ...