Intrastratum Counterbalancing: A Procedure to Improve the Precision of Stratified Mean-Per-Unit Estimates in Accounting and Auditing

In accounting and auditing, critical monetary estimation applications based on sampling often rely on stratified mean-per-unit (SMPU) sampling due to the technique’s unique ability to produce trustworthy confidence intervals when applied to low-error populations. Although reliable, SMPU yields less precise confidence intervals than other estimation techniques. To address this weakness, we present and test a data transformation procedure for use with SMPU- Intrastratum Counterbalancing . After strata boundaries are finalized but prior to sample selection, this procedure creates new sampling units in each stratum by counterbalancing original stratum population elements one or more times. As a result, the number of strata sampling units and strata standard deviations are reduced. These changes reduce the SMPU estimator standard deviation thereby improving precision. In simulations using real accounting populations, counterbalancing produced large improvements in precision. Compared to SMPU without counterbalancing, one application of counterbalancing produced a 52% improvement in mean precision while a second application produced a 73% improvement in mean precision. These improvements were achieved with no change in the number of original population elements examined and suggest that use of Intrastratum Counterbalancing would be beneficial in many SMPU estimation applications. Equations are provided for planning Intrastratum Counterbalancing applications.