National Heart & Lung Institute, Imperial College London, UK.
J Clin Epidemiol. 2009 Dec;62(12):1242-7. doi: 10.1016/j.jclinepi.2009.02.004. Epub 2009 Apr 23.
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.
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.
Over the range of pre-study powers typical in published research, the Bayesian interpretation of a given P-value varies little with power.
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.
如果检验的效能高，则低 P 值为真实效应提供了更有说服力的证据，这一点被反复提及。然而，这一观点基于一种论点，该论点忽略了确切的 P 值，而只是简单地观察 P 是否小于某个截止值，并且简化了可能的效应大小。在非贝叶斯框架中，有充分的理由认为效能不会影响特定 P 值的证据。在这里，我在现实情况下说明了研究前效能与 P 值的贝叶斯解释之间的关系。
使用效应大小的常规先验分布和样本估计的抽样分布的正态逼近进行贝叶斯计算，其中数据是确切的 P 值。
在发表研究中典型的研究前效能范围内，给定 P 值的贝叶斯解释随效能变化很小。
具有合理假设的贝叶斯分析得出的结果与更简单的非贝叶斯直觉非常吻合，即精确 P 值提供的对零假设的证据不应依赖于效能。
