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J Clin Epidemiol. 2009 Dec;62(12):1242-7. doi: 10.1016/j.jclinepi.2009.02.004. Epub 2009 Apr 23.

The Bayesian interpretation of a P-value depends only weakly on statistical power in realistic situations.

Author information

1
National Heart & Lung Institute, Imperial College London, UK. richard.hooper2@imperial.ac.uk

Abstract

OBJECTIVE:

It is often repeated that a low P-value provides more persuasive evidence for a genuine effect if the power of the test is high. However, this is based on an argument which ignores the precise P-value in favor of simply observing whether P is less than some cut-off, and which oversimplifies the possible effect sizes. In a non-Bayesian framework, there are good reasons to think that power does not affect the evidence of a given P-value. Here I illustrate the relationship between pre-study power and the Bayesian interpretation of a P-value in realistic situations.

STUDY DESIGN AND SETTING:

A Bayesian calculation, using a conventional prior distribution for the effect size and a normal approximation to the sampling distribution of the sample estimate, where the datum is the precise P-value.

RESULTS:

Over the range of pre-study powers typical in published research, the Bayesian interpretation of a given P-value varies little with power.

CONCLUSION:

A Bayesian analysis with reasonable assumptions produces results remarkably in line with a more simple, non-Bayesian intuition-that the evidence against the null hypothesis provided by a precise P-value should not depend on power.

PMID:
19398295
DOI:
10.1016/j.jclinepi.2009.02.004
[Indexed for MEDLINE]
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