title: Intraclass Correlations and Covariate Outcome Correlations for Planning Two- and Three-Level Cluster-Randomized Experiments in Education.
abstract: BACKGROUND
  Cluster-randomized experiments that assign intact groups such as schools or school districts to treatment conditions are increasingly common in educational research. Such experiments are inherently multilevel designs whose sensitivity (statistical power and precision of estimates) depends on the variance decomposition across levels. This variance decomposition is usually summarized by the intraclass correlation (ICC) structure and, if covariates are used, the effectiveness of the covariates in explaining variation at each level of the design.
  
  
  OBJECTIVE
  This article provides a compilation of school- and district-level ICC values of academic achievement and related covariate effectiveness based on state longitudinal data systems. These values are designed to be used for planning group-randomized experiments in education. The use of these values to compute statistical power and plan two- and three-level group-randomized experiments is illustrated.
  
  
  METHODS
  We fit several hierarchical linear models to state data by grade and subject to estimate ICCs and covariate effectiveness. The total sample size is over 4.8 million students. We then compare our average of state estimates with the national work by Hedges and Hedberg.
authors.affiliation: Institute for Policy Research at Northwestern University, Evanston, IL, USA l-hedges@northwestern.edu.
authors.forename: Larry V
authors.initials: LV
authors.lastname: Hedges
authors.affiliation: Sanford School of Social and Family Dynamics at Arizona State University, Tempe, AZ, USA NORC at the University of Chicago, Chicago, IL, USA.
authors.forename: E C
authors.initials: EC
authors.lastname: Hedberg
keywords: content area; education; methodological development