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Living with p values: resurrecting a Bayesian perspective on frequentist statistics
Sander Greenland1, Charles Poole
1Department of Epidemiology, University of California, Los Angeles, CA, USA. lesdomes@ucla.edu
Epidemiology (Cambridge, Mass.)
|December 13, 2012
Summary
Misinterpreted P values can be better understood using Bayesian interpretations, offering a more accurate approach to statistical analysis than traditional significance testing. This method improves the understanding of probability and statistical findings.
Area of Science:
- Statistics
- Bayesian Inference
- Hypothesis Testing
Background:
- P values are widely misused and misinterpreted in scientific literature, despite calls to discourage their use.
- Common misinterpretations include viewing P values as the probability of a null hypothesis being true or of a finding being due to chance.
Purpose of the Study:
- To demonstrate how Bayesian interpretations can correct common misuses of P values.
- To propose a modern statistical analysis framework that emphasizes fit, distance, and posterior probability over traditional significance testing.
Main Methods:
- Applying Bayesian principles to common statistical measures like confidence intervals and P values.
- Illustrating how weak priors can lead to Bayesian approximations of frequentist measures.
- Exploring the relationship between one-sided P values and posterior probabilities under specific conditions.
Main Results:
- Under weak priors, 95% confidence intervals approximate 95% posterior probability intervals.
- One-sided P values can approximate directional posterior probabilities.
- A one-sided P value can serve as a lower bound for the posterior probability of a point estimate being on the wrong side of a prior median.
Conclusions:
- Bayesian interpretations offer a more accurate understanding of P values, mitigating widespread misinterpretations.
- A modern statistical framework incorporating Bayesian concepts can replace traditional accept/reject decisions with more informative measures.
- This approach enhances the rigor and clarity of statistical reporting in scientific research.
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