Challenges in Statistical Validation: Introducing Practical Significance Probability as an Alternative

For decades, researchers have relied on P-values and Null Hypothesis Significance Testing (NHST) to assess statistical significance. Despite their widespread use, these methods have faced criticism due to common misunderstandings, arbitrary thresholds, and oversimplified interpretations, contributing to the replication crisis in scientific research. Recent proposals to address these limitations include lower significance levels, confidence intervals, effect sizes, Bayesian methods, and hybrid approaches. However, none has fully replaced NHST. In this thesis, we reviewed key critiques of traditional statistical methods and introduced a new metric called Practical Significance Probability (PSP). PSP estimates the probability that an observed effect exceeds a predefined threshold of practical importance. It combines both effect size and uncertainty into a single intuitive measure, shifting emphasis from purely statistical significance toward practical or real-world importance. To evaluate PSP’s performance, we conducted empirical simulations inspired by previous research. The analysis showed that PSP effectively reduces false positives (6.6%) compared to traditional NHST methods (37% false positives with alpha = 0.05). PSP's continuous probability-based approach promotes a nuanced interpretation rather than rigid, binary decisions about statistical significance. We conclude that PSP is an easy-to-learn, intuitive, and effective tool for researchers, complementing rather than replacing existing methods. It helps researchers prioritize real-world relevance, facilitating more meaningful conclusions in scientific research.