Nonparametric combination (NPC): A framework for testing elaborate theories

Social scientists are commonly advised to deduce and test all observable implications of their theories. We describe a principled framework for testing such "elaborate" theories: nonparametric combination. Nonparametric combination (NPC) assesses the joint probability of observing the theoretically predicted pattern of results under the sharp null of no effects. NPC accounts for the dependence among the component tests without relying on modeling assumptions or asymptotic approximations. Multiple-testing corrections are also easily implemented with NPC. As we demonstrate with four applications, NPC leverages theoretical knowledge into greater statistical power, which is particularly valuable for studies with strong research designs but small sample sizes. We implement these methods in a new R package, NPC.