Ratio and proportional relationships are of primary importance during the upper elementary and middle school grades (Kilpatrick, Swafford, & Findell, 2001; National Council of Teachers of Mathematics, 1989, 2000; National Mathematics Advisory Panel [NMAP], 2008). These relationships, along with the interrelated topics of fractions, decimals,…

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.…