A valuable extension of the single-rating regression discontinuity design (RDD) is a multiple-rating RDD (MRRDD). To date, four main methods have been used to estimate average treatment effects at the multiple treatment frontiers of an MRRDD: the "surface" method, the "frontier" method, the "binding-score" method, and…

This paper 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. Part I of the paper introduces the concepts, issues, and options involved. Parts II and III present empirical findings…