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.…

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.…

In this article, the authors present and test a formal model that holds that people use information about category boundaries in estimating inexactly represented stimuli. Boundaries restrict stimuli that are category members to fall within a particular range. This model posits that people increase the average accuracy of stimulus estimates by…