Causal inference from 2K factorial designs by using potential outcomes

Abstract

A framework for causal inference from two-level factorial designs is proposed, which uses potential outcomes to define causal effects. The paper explores the effect of non-additivity of unit level treatment effects on Neyman's repeated sampling approach for estimation of causal effects and on Fisher's randomization tests on sharp null hypotheses in these designs. The framework allows for statistical inference from a finite population, permits definition and estimation of estimands other than 'average factorial effects' and leads to more flexible inference procedures than those based on ordinary least squares estimation from a linear model.