This paper presents a counterintuitive result regarding the estimation of a regression slope co-efficient. 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 paper came from noting that the precision of slope estimators deteriorated when pooling baseline predictors across treatment groups.
Keywords: Jensen’s inequality; moderator analysis; pooled variance estimator; ratio estimator.