Causal Inference from Two-level Factorial Designs

The investigators develop a framework for causal inference from two-level factorial and fractional factorial designs with particular sensitivity to applications to social, behavioral and biomedical sciences. The framework utilizes the concept of potential outcomes that lies at the center stage of causal inference and extends Neyman's repeated sampling approach for estimation of causal effects and randomization tests based on Fisher's sharp null hypothesis to the case of 2-level factorial experiments. The framework allows for statistical inference from a finite population, permits definition and estimation of parameters other than ``average factorial effects'' and leads to more flexible inference procedures than those based on ordinary least squares estimation from a linear model. It also ensures validity of statistical inference when the investigation becomes an observational study in lieu of a randomized factorial experiment due to randomization restrictions.

Factorial designs allow efficient and cost-effective assessments of the relative effects of several factors and their interactions on output variables of interest. Such designs have been successfully applied in several scientific, engineering and industrial endeavors, but not often used in the social, behavioral or biomedical sciences in spite of several potential applications in these fields. The proposed methodology addresses the complications associated with multi-factor experiments in the aforesaid fields and has a wide range of applications. It can be applied, for example, to assess the impact of several new initiatives on high-school education; or to conduct cost-effective clinical trials to study individual and combined effects of different treatments offered to patients suffering from a certain disease; or to identify critical factors that affect yield of complex physical processes in material science like synthesis of nanostructures. It can also be applied to comparative effectiveness research (e.g., in evidence-based medicine).