Abstract

Much of the blame for failed attempts to replicate reports of scientific findings has been placed on ubiquitous and persistent misinterpretations of the p value. An increasingly popular solution is to transform a two-sided p value to a lower bound on a Bayes factor. Another solution is to interpret a one-sided p value as an approximate posterior probability. Combining the two solutions results in confidence intervals that are calibrated by an estimate of the posterior probability that the null hypothesis is true. The combination also provides a point estimate that is covered by the calibrated confidence interval at every level of confidence. Finally, the combination of solutions generates a two-sided p value that is calibrated by the estimate of the posterior probability of the null hypothesis. In the special case of a 50% prior probability of the null hypothesis and a simple lower bound on the Bayes factor, the calibrated two-sided p value is about (1 – abs(2.7 p ln p)) p + 2 abs(2.7 p ln p) for small p. The calibrations of confidence intervals, point estimates, and p values are proposed in an empirical Bayes framework without requiring multiple comparisons.

摘要

对复制科学发现报告的失败尝试的大部分归咎于对p值的普遍存在和持续的误解。一种越来越流行的解决方案是将双边p值转换为贝叶斯因子的下限。另一种解决方案是将单边p值解释为近似后验概率。组合这两个解决方案会产生置信区间，该置信区间通过零假设为真的后验概率估计值进行校准。该组合还提供了一个点估计，该点估计在每个置信水平下都被校准的置信区间所覆盖。最后，解决方案的组合生成双边p由原假设的后验概率估计值校准的值。在零假设的 50% 先验概率和贝叶斯因子的简单下界的特殊情况下，校准的两侧p值约为 (1 – abs(2.7 p ln p )) p  + 2 abs(2.7 p ln p ) 对于小p。置信区间、点估计和p值的校准是在经验贝叶斯框架中提出的，不需要多重比较。