title: A Paradoxical Result in Estimating Regression Coefficients.
abstract: 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.
authors.affiliation: Professor in the Department of Mathematics and Statistics, Wright State University, Day-ton, Ohio 45435.
authors.forename: Thaddeus
authors.initials: T
authors.lastname: Tarpey
authors.affiliation: Professor in the Department of Biostatistics, Mailman School of Public Health, Columbia University, New York, NY 10032.
authors.forename: R Todd
authors.initials: RT
authors.lastname: Ogden
authors.affiliation: Associate Professor in the Department of Child and Adolescent Psychiatry, New York University, New York, NY 10016-6023 and a Senior Researcher at the Nathan S. Kline Institute for Psychiatric Research, Orangeburg, NY 10962.
authors.forename: Eva
authors.initials: E
authors.lastname: Petkova
authors.affiliation: Professor in the Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 8713.
authors.forename: Ronald
authors.initials: R
authors.lastname: Christensen
keywords: Jensen’s inequality; moderator analysis; pooled variance estimator; ratio estimator