Causal Inference and Statistical Fallacies

Abstract

Fallacies are defined as plausible-seeming arguments that give the wrong conclusion. The article concentrates on those with some connection with causality. The classical definition of causality involving a necessary and sufficient condition for an effect is rejected and three possible definitions discussed. The first is that of a statistical association that cannot be explained away as the effect of admissible alternative features. To make this more precise, Markov graphical representations are introduced and the important distinction between pairs of variables on an equal footing and those in a potential explanatory-response relation described. The roles of unobserved confounders and of randomization are outlined. A second interventionist or counterfactual notion of causality is described. This in particular excludes as potential causes intrinsic features of the individuals under study. The role of variables intermediate between the potential cause and the ultimate response is discussed. Finally a third notion of causality involving some understanding of process underlying the relation in question is given. Fallacies connected with various steps in the argument are briefly mentioned. Finally three special fallacies are discussed in slightly more detail. One is connected with inappropriate probability calculations, a second with the role of interactions, and a third with the Yule–Simpson paradox. Some suggestions for further reading are given.