On Randomization-based and Regression-based Inferences for 2^K Factorial Designs

TL;DR

This paper extends the causal inference framework for 2^K factorial designs, showing the equivalence of regression-based and randomization-based inferences, and justifies the use of regression methods from a finite-population perspective.

Contribution

It generalizes the randomization-based causal inference framework to 2^K factorial designs and establishes their equivalence with regression-based inferences.

Findings

Regression-based and randomization-based inferences are equivalent for 2^K factorial designs.

Regression methods are justified from a finite-population perspective in factorial experiments.

The framework extends previous causal inference methods to more complex factorial designs.

Abstract

We extend the randomization-based causal inference framework in Dasgupta et al. (2015) for general 2^K factorial designs, and demonstrate the equivalence between regression-based and randomization-based inferences. Consequently, we justify the use of regression-based methods in 2^K factorial designs from a finite-population perspective.