Détente: A Practical Understanding of P values and Bayesian Posterior Probabilities

Area of Science:

• Statistics
• Biostatistics
• Scientific Inference

Background:

• Null hypothesis significance testing (NHST) with P < 0.05 has been standard in scientific reporting.
• Historically, statistically significant findings were equated with scientific or clinical importance.
• Challenges to NHST have persisted for decades but often overlooked.

Purpose of the Study:

• To clarify the fundamental differences between frequentist (NHST) and Bayesian statistical inference.
• To address the confusion and controversy surrounding P values and statistical significance.
• To demonstrate the harmonious coexistence of NHST and Bayesian approaches in clinical trial design and inference.

Main Methods:

• Explanation of the core distinction: frequentist P value as pr(A|B) vs. Bayesian posterior probability as pr(B|A).
• Discussion of historical and contemporary debates between frequentist and Bayesian schools of thought.
• Analysis of the impact of recent statements from organizations like the American Statistical Association.

Main Results:

• Many scientists and statisticians lack a clear conceptual understanding of the differences between NHST and Bayesian methods.
• This lack of understanding fuels confusion and conflict regarding statistical interpretation.
• The paper elucidates the distinct probabilities calculated by each approach: pr(A|B) for frequentist and pr(B|A) for Bayesian.

Conclusions:

• A clear grasp of the fundamental differences between frequentist and Bayesian statistics is essential.
• Bayesian inference provides a method to quantify the credibility of scientific findings.
• NHST and Bayesian approaches can be integrated to enhance clinical trial design and interpretation.