Strategic Sampling, Physical Units Sampling, and Dollar Units Sampling - Hansen, Stephen C. (The Accounting Review, 1993)
[One of the most common decisions facing an internal auditor is choosing which line items to investigate. An extensive literature (Dworin and Grimlund 1984; Leslie et al. 1980; Menzefricke 1984; Teitlebaum and Robinson 1975) deals with the statistical and decision-theoretic aspects of his choice. This paper expands on previous work by adding a strategic source of errors: dishonest employees. It addresses the question of how the presence of strategic errors affects the relationship between the auditor's testing strategy and item value. I show that incorporating strategic errors can lead to audit strategies similar to Physical Units and Dollar Units Sampling. I highlight the assumptions driving the results by contrasting a firm's (or internal auditor's) use of an optional test in four stylized models of accounts receivable. The first model examines the firm's behavior when faced with non-strategic (statistical) billing errors. In this model the accounting system generates random errors that result in over- or underbilling customers. The firm can use a costly, imperfect test to remove errors before the bills are sent out. In this nonstrategic model the firm randomizes and tests an item if and only if the benefit is greater than the cost. Because the amount of billing error is unrelated to the item value, there is no clear link between the firm's testing decision and the value of the line item. The second billing model adds the possible existence of dishonest employees who can steal from line items. A dishonest employee makes two decisions. He decides whether to steal from the line item, and, if he steals, he chooses the amount of the theft. A dishonest employee would steal the entire item if he were certain that the firm would never test that item. The dishonest employee's behavior forces the firm to consider the value of the item in determining the region of untested items. Specifically, low value items are never tested. As in many strategic models, the interaction with dishonest employees may lead to randomization. In particular, the randomized testing strategy can look like Stratified Physical Units Attributes Sampling (Leslie et al. 1980). The firm sorts items into different groups and each item in a group has the same probability of being tested. The third model contains only the statistical errors of incorrectly adding or deleting a sales discount, a percentage of the item value. Since the testing gain is directly related to the value of the line item, the firm's strategy depends on an item's value. The firm always tests high value items, and never tests low value items. The fourth model adds potentially dishonest employees who can provide unearned sales discounts to their confederates. In this model the firm stratifies items into three groups. It never investigates small items, always investigates large items, and randomizes over intermediate value items with probabilities roughly proportionate to the value of the item. This procedure is similar to a common audit procedure, Dollar Unit Cell Width Sampling (Leslie et al. 1980).]