Attribute Sampling: A Belief-Function Approach to Statistical Audit Evidence

The Dempster-Shafer belief function framework has been used to model the aggregation of audit evidence based on subjectively assessed beliefs. This paper shows how statistical evidence obtained by means of attribute sampling may be represented as belief functions, so that it can be incorporated into such models. In particular, the article shows: (1) how to determine the sample size in attribute sampling to obtain a desired level of belief that the true attribute occurrence rate of the population lies in a given interval; (2) what level of belief is obtained for a specified interval, given the sample result. As intuitively expected, we find that the sample size increases as the desired level of belief in the interval increases. In evaluating the sample results, our findings are again intuitively appealing. For example, provided the sample occurrence rate falls in the interval B for a given number of occurrences of the attribute, we find that the belief in B, Bel(B), increases as the sample size increases. However, if the sample occurrence rate falls outside of the interval, then Bel(B) is zero. Note that, in general, both Bel(B) and Bel(notB) are zero when the sample occurrence rate falls at the end points of the interval. These results extend similar results already available for variables sampling. However, the auditor faces an additional problem for attribute sampling: how to convert belief in an interval for control exceptions into belief in an interval for material misstatements in the financial statements, so that it can be combined with evidence from other sources in implementations of the Audit Risk Model.