Causal inference from $2^k$ factorial designs using the potential outcomes model

TL;DR

This paper develops a new framework for causal inference in 2-level factorial experiments using potential outcomes, enabling flexible, finite-population-based analysis beyond traditional linear models.

Contribution

It extends Neyman's and Fisher's methods to factorial designs, allowing for diverse estimands and more adaptable inference procedures.

Findings

Framework enables causal inference from finite populations.

Allows estimation of various factorial effects.

Provides more flexible inference than linear models.

Abstract

A framework for causal inference from two-level factorial designs is proposed. 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 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.