The p–fr–nb triplet: a unified framework for statistical fragility and robustness across clinical study designs

Clinical studies commonly report p-values but rarely quantify how stable those p-values are or how far the observed data lie from the point representing no effect. This study introduces a unified framework that evaluates statistical significance, fragility, and neutrality distance across three standard clinical data structures: single-arm binomial outcomes, two-arm binary outcomes, and continuous two-group outcomes. The objective was to determine whether reporting these three components together can improve the interpretation of clinical research results. Using previously published summary statistics, we calculated significance, fragility, and neutrality distance for representative examples from each design category. The framework applies the diagnostic fragility quotient and a proportion-based neutrality measure for single-arm benchmarks; the global fragility quotient and risk quotient for two-arm binary outcomes; and the continuous fragility scale and meaningful change index for mean comparisons. Across all examples, the triplet revealed patterns that were not detectable with p-values or effect sizes alone. Some statistically significant findings were highly fragile or close to neutrality despite appearing reliable. At the same time, some non-significant results showed meaningful separation from the no-effect state despite stable p-values. These findings highlight how statistical significance, decision stability, and distance from neutrality represent distinct dimensions of evidence that can diverge in clinically important ways. This triplet provides a concise, generalizable summary of evidence quality that enhances transparency and reduces misinterpretation across a broad range of study designs.