A Paradoxical Result in Estimating Regression Coefficients

Abstract

This article presents a counterintuitive result regarding the estimation of a regression slope coefficient. Paradoxically, the precision of the slope estimator can deteriorate when additional information is used to estimate its value. In a randomized experiment, the distribution of baseline variables should be identical across treatments due to randomization. The motivation for this article came from noting that the precision of slope estimators deteriorated when pooling baseline predictors across treatment groups.

• Jensen’s inequality
• Moderator analysis
• Pooled variance estimator
• Ratio estimator