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Bayes factor and posterior probability: Complementary statistical evidence to p-value.

Ruitao Lin¹, Guosheng Yin¹

¹Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong.

Contemporary Clinical Trials

|July 28, 2015

Summary

This summary is machine-generated.

The p-value in hypothesis testing is hard to interpret as evidence against the null hypothesis. Bayesian posterior probability offers a clearer measure of evidence, revealing the null hypothesis may still be likely even when rejected.

Keywords:

Bayes factor Bayesian inference Frequentist hypothesis testing Posterior probability p-value

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Area of Science:

Statistics
Bayesian inference
Hypothesis testing

Background:

The p-value is a conventional metric in hypothesis testing, typically compared against a 0.05 significance level to decide on null hypothesis rejection.
Interpreting the p-value as a direct measure of evidence against the null hypothesis or the probability of the null being true is challenging.

Purpose of the Study:

To compare the interpretability and utility of the p-value with Bayesian posterior probability in hypothesis testing.
To highlight the limitations of p-values in quantifying evidence against the null hypothesis.

Main Methods:

Comparative analysis of p-values and Bayesian posterior probabilities.
Utilized a recent clinical trial to illustrate the comparison.

Main Results:

Even when the null hypothesis is rejected based on p-values, there can be a substantial posterior probability (e.g., ~20%) that the null hypothesis is actually true.
P-values only indicate the probability of observing data under the null hypothesis, not the probability of the null hypothesis itself.

Conclusions:

The p-value provides only partial information in hypothesis testing.
Bayesian posterior probability and Bayes factors offer complementary evidence, providing a more comprehensive understanding of the data's support for or against the null hypothesis.