Beyond P-Values: A Comparative Framework For Estimation-Based Inference Using The A Priori Procedure And Gain-Probability Analysis

Abstract

This talk compares three inferential paradigms—Null Hypothesis Significance Testing (NHST), the A Priori Procedure (APP), and Gain–Probability (G–P) analysis—highlighting a conceptual shift from binary hypothesis testing toward estimation-based and probabilistic inference. While NHST relies on p-values and post hoc decision rules, APP ensures pre-data estimation reliability, and G–P quantifies the probability of one outcome exceeding another. The comparative analysis and schematic illustrate how APP and G–P, introduced by Trafimow and Wang, align with the broader re-producibility reform emphasizing estimation, transparency, and interpretive meaning. Together, these frameworks offer a coherent alternative to significance testing by focusing on precision, probability, and practical understanding of effects. Real data applications of the APP and G-P analysis are given for illustrations of our proposed methods.

By Tonghui Wang, Boris S.T. Choy and David Trafimow

Tonghui Wang, Professor of Statistics, Chair of Graduate Studies Committee, Department of Mathematical Sciences, New Mexico State University.