A Note on Computing Upper Error Limits in Dollar-Unit Sampling

Abstract

The method of dollar-unit sampling (D US) has been advocated by many authors in the accounting and auditing literature during the 1970s (e.g., Anderson and Teitlebaum [1973], Kaplan [1975]). One reason for its popularity is its ability to handle auditing populations with very low error rates, where normal-based statistical sampling procedures fail to give reasonable error limits. The issue of error limits for DUS has been considered by several authors. Anderson and Teitlebaum [1973] used a nonclassical evaluation procedure suggested by Stringer [1963]. A critical view of this method is found in Goodfellow, Loebbecke, and Neter [1974]. Among other things, it seems unduly conservative. Neter, Leitch, and Fienberg [1978] have given error limits based on the multinomial distribution. These are nonparametric in nature and are definitely less conservative than the Stringer bounds. Even tighter bounds may be obtained by assuming a particular (parametric) model for the error structure. Garstka [1977] has suggested the use of a compound Poisson process as a model for the combined error rates and size of error, that is, he assumes that the number of sampled erroneous dollar units follows a Poisson distribution. His analysis is based on the specific assumption that the number of error-units (say, ten-cent units) in an erroneous dollar unit follows a geometric distribution. The intent of his article was not to