Improved Neymanian analysis for $2^K$ factorial designs with binary outcomes

TL;DR

This paper introduces an improved Neymanian variance estimator for $2^K$ factorial designs with binary outcomes, reducing over-estimation and providing more accurate inference under the potential outcomes framework.

Contribution

It derives the sharp lower bound of the sampling variance and proposes an improved variance estimator for factorial effects in binary outcome experiments.

Findings

The improved estimator reduces over-estimation of variance.

It provides more accurate confidence intervals for factorial effects.

The method is applicable within the potential outcomes framework.

Abstract

$2^K$ factorial designs are widely adopted by statisticians and the broader scientific community. In this short note, under the potential outcomes framework (Neyman, 1923; Rubin, 1974), we adopt the partial identification approach and derive the sharp lower bound of the sampling variance of the estimated factorial effects, which leads to an "improved" Neymanian variance estimator that mitigates the over-estimation issue suffered by the classic Neymanian variance estimator by Dasgupta et al. (2015).