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

$2^K$ 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).