Title: Tables with Critical Values for the Meta-Analysis of Genuine and Fake $\boldsymbol{p}$-Values Show Chinese title

Title: 包含真实和虚假$\boldsymbol{p}$值元分析临界值的表格

Abstract: The classical theory for the meta-analysis of $p$-values is based on the assumption that if the overall null hypothesis is true, then all $p$-values used in a chosen combined test statistic are genuine, i.e., are observations from independent and identically distributed standard uniform random variables. However, the pressure felt by most researchers to publish, which is worsen by publication bias, can originate fake $p$-values to be reported, usually Beta(1,2) distributed. In general, the existence of fake $p$-values in a sample of $p$-values to be combined is unknown, and if, for some reason, there is information that they do exist, their number will most likely be unknown as well. Moreover, even if fake $p$-values are accounted for, the cumulative distribution function of classical combined test statistics does not have a closed-form expression that facilitates its practical usage. To overcome this problem, tables with estimated critical values are supplied for the commonly used combined tests for the meta-analysis of $p$-values when a few of them are fake ones, i.e., Beta(1,2) distributed. Show Chinese abstract

Abstract: 元分析的$p$值的经典理论基于这样的假设：如果总体零假设为真，那么在选定的联合检验统计量中使用的所有$p$值都是真实的，即来自独立同分布的标准均匀随机变量的观测值。 然而，大多数研究人员面临的发表压力，加上发表偏倚，可能导致报告虚假的$p$值，通常服从Beta(1,2)分布。 一般来说，在要合并的$p$值样本中是否存在虚假的$p$值是未知的，而且如果由于某种原因有信息表明它们存在，其数量也很可能未知。 此外，即使考虑了虚假的$p$值，经典联合检验统计量的累积分布函数也没有一个便于实际使用的闭式表达式。 为了克服这个问题，当其中一些是虚假值（即服从Beta(1,2)分布）时，为元分析的$p$值的常用联合检验提供了估计临界值的表格。