Beyond p-values: Rethinking Statistical Frameworks for Addressing the Replication Crisis

The replication crisis across scientific disciplines has prompted critical examination of statistical practices underpinning empirical research. This chapter analyzes how significance testing contributes to replication challenges through the lens of the TASI (Theoretical, Auxiliary, Statistical, Inferential) model. We examine three distinct contexts—inferential knowledge, region of acceptance testing, and statistical learning—to identify limitations in conventional significance testing and propose alternative frameworks. We argue that most problems with significance testing stem from researchers' tendencies to confirm rather than falsify hypotheses, regardless of statistical approach. We introduce REACT (Region of Acceptance Testing) as a stronger alternative to p-values, offering a structured decision-making process that integrates effect sizes and confidence intervals while explicitly recognizing when data is insufficient for definitive conclusions. Additionally, we propose Generalized Additive Models for Location, Scale, and Shape (GAMLSS) as a comprehensive statistical learning framework that transcends traditional hypothesis testing, focusing instead on descriptive, explanatory, and predictive modeling. The chapter ends with a concise exploration of the connection between data science and artificial intelligence.