Designing Efficient Stratified Mean-Per-Unit Sampling Applications in Accounting and Auditing

Despite technological advances in accounting systems and audit techniques, sampling remains a commonly used audit tool. For critical estimation applications involving low error rate populations, stratified mean-per-unit sampling (SMPU) has the unique advantage of producing trustworthy confidence intervals. However, SMPU is less efficient than other classical sampling techniques because it requires a larger sample size to achieve comparable precision. To address this weakness, we investigated how SMPU efficiency can be improved via three key design choices: (a) stratum boundary selection method, (b) number of sampling strata, and (c) minimum stratum sample size. Our tests disclosed that SMPU efficiency varies significantly with stratum boundary selection method. An iterative search-based method yielded the best efficiency, followed by the Dalenius-Hodges and Equal-Value-Per-Stratum methods. We also found that variations in Dalenius-Hodges implementation procedures yielded meaningful differences in efficiency. Regardless of boundary selection method, increasing the number of sampling strata beyond levels recommended in the professional literature yielded significant improvements in SMPU efficiency. Although a minor factor, smaller values of minimum stratum sample size were found to yield better SMPU efficiency. Based on these findings, suggestions for improving SMPU efficiency are provided. We also present the first known equations for planning the number of sampling strata given various application-specific parameters.