Abstract Hypothesis tests are conducted not only to determine whether a null hypothesis (H0) is true but also to determine the direction or sign of an effect. A simple estimate of the posterior probability of a sign error is PSE = (1 – PH0)p/2 + PH0, depending only on a two-sided p-value and PH0, an estimate of the posterior probability of H0. A convenient option for PH0 is the posterior probability derived from estimating the Bayes factor to be its e p ln lower bound. In that case, PSE depends only on p and an estimate of the prior probability of H0. PSE provides a continuum between significance testing and traditional Bayesian testing. The former effectively assumes the prior probability of H0 is 0, as some statisticians argue. In that case, PSE is equal to a one-sided p-value. (In that sense, PSE is a calibrated p-value.) In traditional Bayesian testing, on the other hand, the prior probability of H0 is at least 50%, which usually brings PSE close to PH0.

中文翻译：

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通过估计符号错误的概率来解释和校准零假设显着性检验：贝叶斯频率论连续统

摘要 进行假设检验不仅可以确定零假设 (H0) 是否为真，还可以确定效果的方向或符号。符号错误后验概率的简单估计是 PSE = (1 – PH0)p/2 + PH0，仅取决于两侧 p 值和 PH0，即 H0 后验概率的估计。PH0 的一个方便选项是通过将贝叶斯因子估计为其 ep ln 下界得出的后验概率。在这种情况下，PSE 仅取决于 p 和 H0 的先验概率的估计。PSE 提供了显着性检验和传统贝叶斯检验之间的连续统。正如一些统计学家争论的那样，前者有效地假设 H0 的先验概率为 0。在这种情况下，PSE 等于单边 p 值。（从这个意义上说，PSE 是一个校准的 p 值。