[Paper Review] Causal inference from $2^k$ factorial designs using the potential outcomes model

Tirthankar Dasgupta, Natesh S. Pillai+1 more|arXiv (Cornell University)|Nov 11, 2012

Optimal Experimental Design Methods17 references16 citations

TL;DR

This paper proposes a causal inference framework for 2^k factorial designs using the potential outcomes model, extending Neyman’s repeated sampling and Fisher’s randomization tests to enable finite-population inference. It supports estimation of non-average estimands and offers more flexible inference than OLS, enhancing causal identification in factorial experiments.

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 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.

Motivation & Objective

• To develop a causal inference framework for 2^k factorial experiments grounded in the potential outcomes model.
• To extend Neyman’s repeated sampling approach and Fisher’s randomization tests to factorial designs.
• To enable inference from a finite population rather than relying on large-sample approximations.
• To support definition and estimation of estimands beyond average factorial effects.
• To provide more flexible inference procedures than those based on ordinary least squares.

Proposed method

• Uses the potential outcomes model as the foundational framework for causal inference.
• Applies Neyman’s repeated sampling approach to estimate causal effects under randomization.
• Employs Fisher’s sharp null hypothesis for randomization-based tests in factorial settings.
• Derives estimands that generalize beyond average factorial effects, such as quantile or distributional effects.
• Constructs test statistics based on randomization distributions to assess significance without distributional assumptions.
• Integrates finite-population inference to improve validity in small-sample factorial experiments.

Experimental results

Research questions

• RQ1 How can potential outcomes be used to define causal estimands in 2^k factorial designs?
• RQ2 What is the role of randomization-based inference in factorial experiments under the potential outcomes framework?
• RQ3 Can estimands other than average factorial effects be meaningfully defined and estimated in such designs?
• RQ4 How does the proposed framework improve upon OLS-based inference in terms of flexibility and assumptions?
• RQ5 What are the implications of finite-population inference for causal inference in factorial experiments?

Key findings

• The framework enables causal inference in 2^k factorial designs using the potential outcomes model, ensuring methodological coherence with modern causal inference principles.
• Randomization-based inference under Fisher’s sharp null hypothesis is extended to factorial designs, allowing valid p-values without distributional assumptions.
• Estimands other than average factorial effects—such as quantile or distributional effects—can be defined and estimated within the framework.
• The approach supports finite-population inference, improving relevance and validity in small-sample experimental settings.
• The method provides greater flexibility than OLS by avoiding linear model assumptions and enabling inference on diverse estimands.
• The framework enhances the robustness and interpretability of causal conclusions in factorial experiments through rigorous randomization-based inference.