The precision of estimates of treatment effects in multilevel experiments depends on the sample sizes chosen at each level. It is often desirable to choose sample sizes at each level to obtain the smallest variance for a fixed total cost, that is, to obtain optimal sample allocation. This article extends previous results on optimal allocation to…

Research designs involving cluster randomization are becoming increasingly important in educational and behavioral research. Many of these designs involve two levels of clustering or nesting (students within classes and classes within schools). Researchers would like to compute effect size indexes based on the standardized mean difference to…

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.…

A common mistake in analysis of cluster randomized experiments is to ignore the effect of clustering and analyze the data as if each treatment group were a simple random sample. This typically leads to an overstatement of the precision of results and anticonservative conclusions about precision and statistical significance of treatment effects.…

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…

Experiments that assign intact groups (usually schools) to treatment conditions are increasingly common in educational research. The design of group randomized experiments requires knowledge of the intraclass correlation structure to compute statistical power and to determine the sample sizes required to achieve adequate power. The intraclass…

Four experiments are reported in which people organize a space hierarchically when they estimate particular locations in that space. Earlier work showed that people subdivide circles into quadrants bounded at the vertical and horizontal axes, biasing their estimates towards prototypical diagonal locations within those spatial categories…

Experiments that assign intact groups to treatment conditions are increasingly common in social research. In educational research, the groups assigned are often schools. The design of group-randomized experiments requires knowledge of the intraclass correlation structure to compute statistical power and sample sizes required to achieve adequate…

Research results in the social and behavioral sciences are thought to be less replicable than results in the physical sciences. Comparisons of the cumulativeness of research in the former sciences have not been made. Argues that the study of cumulativeness could predict results from replicated experiments under good conditions. (Author/VM)