Probing the Nature of Inferential Decisions: Fine-Tuning the False Negative Error [β-Risk%]
Year: 2025
Type: article
Abstract: In our experiential-milieu, the False Positive Error [FPE] is the ubiquitous choice used to profile and understand the results of inferential analyses. Rarely, are the False Negative Error [FNE] and its ancestral-derivative: The β-Risk% invited into the Analytical conversation to offer an enrichment of the scope of the inferential-intel used to inform the Decision-Making process. This seems to be the case because usually the FPE-intel is generated from a p-value that effectively is the only inference-intel used by the Analyst. The other FPE-inference-intel derives from Sir R. A. Fisher who suggested that adequate statistical-intel is best created by fixing an a prior specified FPE[α] that marks a Point along the Probability-abscissa forming a binary-partition: A Ho− Non-rejection-zone & Ha− acceptance-zone. This binary-partition invites a What-If-conjecture called the β-Risk% that the p-value inferential-model does not “naturally” facilitate. In practice, we have noticed that the conjectural-feature of creating the β-Risk% has resulted in confusion and invites Gaming of the β-Risk%-intel. We offer a β-Risk%-protocol that, if followed, will enhance the overall decision-impact by partnering the FPE with the FNE. Additionally, in addressing computing the β-Risk%, we offer a discussion of two probability contexts: (i) the population standard deviation σPop is discernable, and (ii) the σPop may be computed. In addition, to facilitate using these ideas in creating inferential-intel, we have programmed these two β-Risk% contexts as stand-alone VBA-Excel Open-access Platforms.
Authors: Moncef Belhadjali, Edward Joseph Lusk
Institutions: Norfolk State University, University of Pennsylvania
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409780344