Binomial Count Information: How Do the Usual Approximations Fare?

Abstract

Focus Decision-making is often aided by examining False Positive Error-risk profiles [FPEs]. In this research report, the decision-making jeopardy that one invites by eschewing the Exact factorial-binomial Probability-values used to form the FPEs in favor of: (i) Normal Approximations [NA], or (ii) Continuity-Corrected Normal Approximations [CCNA] is addressed. Results Referencing an audit context where testing sample sizes for Re-Performance & Re-Calculation protocols are, by economic necessity, in the range of 20 to 100 account items, there are indications that audit decisions would benefit by using the Exact Probability-values. Specifically, using a jeopardy-screen of ±2.5% created by benchmarking the NA & the CCNA by the Exact FPEs, it is observed that: (i) for sample sizes of 100 there is little difference between the Exact and the CCNA FPEs, (ii) almost uniformly for both sample extremes of 20 and 100, the FPEs created using the NA are lower and outside the jeopardy screen, finally (iii) for the CCNA-arm for sample sizes of n = 20, only sometimes are the CCNA FPEs interior to the jeopardy screen. These results call into question not using the Exact Factorial Binomial results. Finally, an illustrative example is offered of an A priori FPE-risk Decision-Grid that can be parametrized and used in a decision-making context.