Decision theory view of auditing;

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A Decision Theory View of Auditing
William L. Felix, Jr.
University of Washington, Seattle
The major objective of the field of applied statistics is to help solve decision problems in the face of uncertainty. This help has traditionally been provided by making inferences based on a probability model. These probability models are the statistician's models of the uncertainty faced by a real world problem-solver. The field of auditing has been the beneficiary over the past ten to fifteen years of increasing assistance from the field of applied statistics. This paper will review these contributions and then consider a new contribution that is a logical next step.
Dealing with Uncertainty
The auditor is continually making choices in the face of uncertainty. The first statistical recognition of this fact occurred with the use of classical statistics in evaluating the results of random sampling.1 The significance of this approach was not that uncertainty was first recognized, but that the risks associated with one particular aspect of auditing were made explicit. That is, the classical state­ment
of confidence interval and level (e.g., ± 50 at 95% confidence) specifies the risk of sampling error.2 Thus one element of the uncertainty faced by an auditor with which he has always had to treat was now disclosed in statistical terms. Given this beginning contribution, expansion of the potential uses of applied statistics to auditing, comparable to other disciplines facing uncertainty, should follow.
In using classical sampling, the contribution of statistics is restricted to the evaluation of evidence obtained by random sampling. Incorporation of this evidence with other evidence is left to the auditor's judgment. More recently a method for combining sample evidence with other auditing evidence has been proposed.3 Inferential methods in Bayesian statistics are based on a posterior probability distribution which is a combination of a prior probability distribu­tion,
representing evidence the auditor has evaluated up to the point of sampling, and a likelihood function, representing the information in the sample. By sub­jectively
specifying the results of evidence evaluated up to a point of time as a probability function, the auditor has expanded the explicit recognition of the uncertainty he faces in carrying out an audit. Again, this uncertainty previously existed but was considered only through intuition and judgment. The advantages for the auditor that result from being more precise in considering risk have been argued by Roberts.4
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