Attribute sampling: A belief-function approach to statistical audit evidence

The Dempster-Shafer belief function framework has been used to model the ag gregation of audit evidence based on subjectively assessed beliefs. This pa per 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 sa mple size in attribute sampling to obtain a desired level of belief that th e 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 increa ses as the desired level of belief in the interval increases. In evaluating the sample results, our findings are again intuitively appealing. For exam ple, provided the sample occurrence rate falls in the interval B for a give n 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 occurre nce 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 resu lts already available for variables sampling. However, the auditor faces an additional problem for attribute sampling: how to convert belief in an int erval for control exceptions into belief in an interval for material missta tements in the financial statements, so that it can be combined with eviden ce from other sources in implementations of the Audit Risk Model.