Misunderstandings among Experimentalists and Observationalists about Causal Inference

We attempt to clarify, and show how to avoid, several fallacies of causal inference in experimental and observational studies. These fallacies concern hypothesis tests for covariate balance between the treated and control groups, and the consequences of using randomization, blocking before randomization, and matching after treatment assignment to achieve balance. Applied researchers in a wide range of scientific disciplines seem to fall prey to one or more of these fallacies. To clarify these points, we derive a new three-part decomposition of the potential estimation errors in making causal inferences. We then show how this decomposition can help scholars from different experimental and observational research traditions better understand each other's inferential problems and attempted solutions. We illustrate with a discussion of the misleading conclusions researchers produce when using hypothesis tests to check for balance in experiments and observational studies