This talk compares three inferential paradigms: Null Hypothesis Significance Testing
(NHST), the A Priori Procedure (APP), and Gain Probability (G-P) analysis, with
the latter two paradigms featuring a conceptual shift away from binary hypothesis
testing toward inference frameworks grounded in estimation and probability. NHST
relies on p-values and dichotomous decision rules; in contrast, APP emphasizes
pre-data estimation reliability, and G-P analysis quantifies the probability that one
outcome exceeds another, and by varying extents. This shift aligns with broader
methodological reforms prioritizing estimation, transparency, and interpretability. In
addition to their conceptual advantages, the APP and G-P paradigms are highly
applicable. To advance this perspective, we examine the derivation of APP for
parameter estimation in linear regression models under skew-normal error structures,
including results on the distribution of regression estimators, supported by simulation
studies and empirical illustrations. We also investigate the G-P framework for gamma distributed
variables in both independent and dependent settings, again reinforced
by simulation studies and real-world applications. Collectively, these frameworks
provide a rigorous and interpretable alternative to conventional significance testing by
prioritizing estimation accuracy, probabilistic interpretation, and practical relevance.