Comparative Performance of Multinomial, Cell, and Stringer Bounds.

Abstract Auditors frequently use monetary-unit sampling. This paper compares the performance of three bounds based on monetary-unit sampling -- the Stringer, cell, and multinomial bounds. The performance of these bounds is also compared with that of a bound based on line-item sampling -- the stratified difference estimator. It is found that the multinomial bound tends to be substantially tighter than the Stringer bound and somewhat tighter than the cell bound when cell sampling is used. The comparatively good performance of the multinomial bound is accompanied by actual confidence levels near or above the nominal level. Though the stratified difference bound tends to be somewhat tighter than the multinomial bound, it has actual confidence levels below the nominal confidence level for the study populations considered. The multinomial bound also performs comparatively well in terms of power characteristics. The probabilities of rejection when the actual total error amount is substantially smaller than materiality are much higher for the Stringer bound and somewhat higher for the cell bound than those for the multinomial bound. Finally, the effect of systematic and cell random selection with monetary-unit sampling is studied when line items in the frame are in approximately random order. Systematic and cell selections tend to improve actual confidence levels for the multinomial bound.