Abstract

As a convention, p-value is often computed in frequentist hypothesis testing and compared with the nominal significance level of 0.05 to determine whether or not to reject the null hypothesis. The smaller the p-value, the more significant the statistical test. Under noninformative prior distributions, we establish the equivalence relationship between the p-value and Bayesian posterior probability of the null hypothesis for one-sided tests and, more importantly, the equivalence between the p-value and a transformation of posterior probabilities of the hypotheses for two-sided tests. For two-sided hypothesis tests with a point null, we recast the problem as a combination of two one-sided hypotheses along the opposite directions and establish the notion of a “two-sided posterior probability,” which reconnects with the (two-sided) p-value. In contrast to the common belief, such an equivalence relationship renders p-value an explicit interpretation of how strong the data support the null. Extensive simulation studies are conducted to demonstrate the equivalence relationship between the p-value and Bayesian posterior probability. Contrary to broad criticisms on the use of p-value in evidence-based studies, we justify its utility and reclaim its importance from the Bayesian perspective.

摘要

作为惯例，通常在频率论假设检验中计算p值，并将其与 0.05 的名义显着性水平进行比较，以确定是否拒绝零假设。p值越小，统计检验越显着。在非信息先验分布下，我们建立了p值与单边检验的原假设贝叶斯后验概率之间的等价关系，更重要的是，p之间的等价关系-value 和两侧检验假设的后验概率的转换。对于具有零点的双边假设检验，我们将问题重新定义为沿相反方向的两个单边假设的组合，并建立了“双边后验概率”的概念，它与（双边) p值。与普遍看法相反，这种等价关系使p值成为对数据支持空值的强度的明确解释。进行了广泛的模拟研究以证明p值和贝叶斯后验概率之间的等价关系。与对p使用的广泛批评相反-在循证研究中的价值，我们证明其效用是合理的，并从贝叶斯的角度重申其重要性。