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Area of Science:

  • Statistics
  • Data Analysis
  • Scientific Methodology

Background:

  • The P value is widely used but frequently misinterpreted in data analysis.
  • Criticism often stems from philosophical and Bayesian perspectives.
  • A properly interpreted P value can serve as evidence against the null hypothesis (H0).

Purpose of the Study:

  • To discuss the correct interpretation of P values and null-hypothesis statistical testing.
  • To address common misinterpretations, such as equating P values with posterior probabilities of H0.
  • To present methods for approximating the posterior probability of H0.

Main Methods:

  • Conceptual discussion of P value meaning and null-hypothesis statistical testing.
  • Explanation of P value as a conditional probability.
  • Introduction of a method to approximate the posterior probability of H0 using P values and prior probabilities.

Main Results:

  • P values are often incorrectly equated with the posterior probability that H0 is true.
  • A lower bound for the posterior probability of H0 can be approximated.
  • When prior uncertainty is high (prior probability of H0 = 0.5), substantially lower P values are needed for strong evidence against H0.

Conclusions:

  • Proper interpretation of P values is crucial to avoid exaggerated claims.
  • The continued use of P values is supported when integrated with data visualization and effect size estimation.
  • Emphasis on understanding the relationship between P values, prior probabilities, and posterior probabilities is recommended.