Global null testing is a classical problem going back about a century to Fisher's and Stouffer's combination tests. In this work, we present simple martingale analogs of these classical tests, which are applicable in two distinct settings: (a) the online setting in which there is a possibly infinite sequence of $p$-values, and (b) the batch setting, where one uses prior knowledge to preorder the hypotheses. Through theory and simulations, we demonstrate that our martingale variants have higher power than their classical counterparts even when the preordering is only weakly informative. Finally, using a recent idea of "masking" $p$-values, we develop a novel interactive test for the global null that can take advantage of covariates and repeated user guidance to create a data-adaptive ordering that achieves higher detection power against structured alternatives.

翻译：全球无效测试是一个古老的问题,可以追溯到大约一个世纪前Fisher和Stouffer的合并测试。在这项工作中,我们展示了这些古典测试的简单的马丁格类比,适用于两种不同的环境:(a) 可能存在无限的美元价值序列的在线环境,和(b) 批量设置,其中一个人利用事先知识来预定假设。我们通过理论和模拟,证明我们的马丁格尔变异体比古典异体拥有更高的权力,即使预定顺序仅提供微弱的信息。最后,我们利用最新的“制表”概念,为全球公体开发了一个新型互动测试,可以利用共变和反复用户指导来创建数据适应秩序,从而针对结构化替代品实现更高的检测能力。