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

The piranha problem: Large effects swimming in a small pond