Using Decision-Theory For Planning Audit Sample-Size With Dollar Unit Sampling

The purpose of this paper is to examine optimal sample size selection for auditing items making up account balances based on some prior information obtained from the study of the system of internal controls and from previous years. The contribution of the paper consists in using dollar unit sampling (DUS) methodology in a formal decision-theoretic approach to this problem.1 I use dollar unit sampling (DUS) because its use by auditing firms is becoming more widespread, and standard normal theory approaches have been found to suffer from lack of robustness in many auditing environments.2 Before proceeding, some terminology needs to be introduced. An auditor is interested in the total value of all the items (or records) that make up the account of interest, for example, an inventory or an accounts receivable account. Each account item has associated with it a book (or recorded) value and an audit value, which is the value an auditor would assign to the item after careful investigation. The tainting of an item is defined to be its relative error, that is: