In some scientific fields, it is common to have certain variables of interest that are of particular importance and for which there are many studies indicating a relationship with different explanatory variables. In such cases, particularly those where no relationships are known among the explanatory variables, it is worth asking under what conditions it is possible for all such claimed effects to exist simultaneously. This paper addresses this question by reviewing some theorems from multivariate analysis showing that, unless the explanatory variables also have sizable dependencies with each other, it is impossible to have many such large effects. We discuss implications for the replication crisis in social science.

翻译：在某些科学领域，经常会出现某些特别重要的兴趣变量，且有大量研究指出它们与各种解释变量存在关联。在这种情况下，特别是当解释变量之间已知无关联时，值得探讨在所有声称的效应能够同时存在的条件下，这是否可能。本文通过回顾多元分析中的一些定理来解答这一问题，这些定理表明，除非解释变量之间也存在显著的相关性，否则不可能同时存在如此多的大效应。我们讨论了这一发现对社会科学复制危机的启示。