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.
Highlights
In a decision-making context, it is critical to have “exact” information to inform the data-analytics so as to arrive at the best decision in the particular context under consideration
The utility of analytic information is related to the acceptance of variation from exact results. With this as the operational mantra, consider the statistical decision making that is very often found in the audit context where the information collected is the Number of Events
The probability density function is scripted as: Bpdf[n, %], Where: n is the number of sampled events from the Account under audit, the Account has N elements—as such, this is the population from which a random sample of size n is taken, and % is the a priori expectation of the percentage of targets or successes in the population of N-individual accounts
Summary
In a decision-making context, it is critical to have “exact” information to inform the data-analytics so as to arrive at the best decision in the particular context under consideration. Experiential streaming feedback over many years instructing Math/Stat courses requires that one clarify what information is generated in a computation domain. In this regard, it is most instructive to consider (i) the measurement of Area in a flat-horizontal plane, and (ii) the Rate of Change of Functional. Assume that one wants to compute the Area of a Space for a flower garden. In this case, there is a flat-tract rectangle of land that is 4-Meters in Length and 2-Meters in Width. The area of this garden is: Area = Length × Width; 8-Squared-Meters = [2-Meters × 4-Meters] No approximation; the computation is exact and so, by definition, useful for the task at hand
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