Using Covariates to Improve Precision for Studies That Randomize Schools to Evaluate Educational Interventions

Abstract
This article examines how controlling statistically for baseline covariates, especially pretests, improves the precision of studies that randomize schools to measure the impacts of educational interventions on student achievement. Empirical findings from five urban school districts indicate that (1) pretests can reduce the number of randomized schools needed for a given level of precision to about half of what would be needed otherwise for elementary schools, one fifth for middle schools, and one tenth for high schools, and (2) school-level pretests are as effective in this regard as student-level pretests. Furthermore, the precision-enhancing power of pretests (3) declines only slightly as the number of years between the pretest and posttests increases; (4) improves only slightly with pretests for more than 1 baseline year; and (5) is substantial, even when the pretest differs from the posttest. The article compares these findings with past research and presents an approach for quantifying their uncertainty.