We obtain several inequalities on the generalized means of dependent p-values. In particular, the weighted harmonic mean of p-values is strictly sub-uniform under several dependence assumptions of p-values, including independence, weak negative association, the class of extremal mixture copulas, and some Clayton copulas. Sub-uniformity of the harmonic mean of p-values has an important implication in multiple hypothesis testing: It is statistically invalid to merge p-values using the harmonic mean unless a proper threshold or multiplier adjustment is used, and this invalidity applies across all significance levels. The required multiplier adjustment on the harmonic mean explodes as the number of p-values increases, and hence there does not exist a constant multiplier that works for any number of p-values, even under independence.

翻译：我们得到了关于相依p值广义均值的若干不等式。特别地，在p值的若干相依假设下，包括独立性、弱负相关性、极值混合连接函数类以及某些Clayton连接函数，p值的加权调和均值严格呈现次均匀性。p值调和均值的次均匀性对多重假设检验有重要启示：除非采用适当的阈值或乘数调整，否则使用调和均值合并p值在统计上是无效的，且此无效性适用于所有显著性水平。随着p值数量的增加，对调和均值所需的乘数调整呈爆炸性增长，因此即使是在独立性假设下，也不存在适用于任意数量p值的常数乘数。