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AbstractRecent advances in statistical methods for meta‐analysis help reviewers to identify systematic variation in research results.

"Employing a variety of analytical methods, The Social Organization of Schooling provides a sound understanding of the social mechanisms at work in our educational system. This volume brings a fresh perspective to the many ongoing debates in education policy and is essential reading for anyone concerned with the future of America's children."--Jacket

Background: Randomized experiments are often considered the strongest designs to study the impact of educational interventions. Perhaps the most prevalent class of designs used in large-scale education experiments is the cluster randomized design in which entire schools are assigned to treatments. In cluster randomized trials that assign schools to treatments within a set of school districts, the statistical power of the test for treatment effects depends on the within-district school-level intraclass correlation (ICC). Hedges and Hedberg (2014) recently computed within-district ICC values in 11 states using three-level models (students in schools in districts) that pooled results across all the districts within each state. Although values from these analyses are useful when working with a representative sample of districts, they may be misleading for other samples of districts because the magnitude of ICCs appears to be related to district size. To plan studies with small or nonrepresentative samples of districts, better information are needed about the relation of within-district school-level ICCs to district size. Objective: Our objective is to explore the relation between district size and within-district ICCs to provide reference values for math and reading achievement for Grades 3–8 by district size, poverty level, and urbanicity level. These values are not derived from pooling across all districts within a state as in previous work but are based on the direct calculation of within-district school-level ICCs for each school district. Research Design: We use mixed models to estimate over 7,000 district-specific ICCs for math and reading achievement in 11 states and for Grades 3–8. We then perform a random effects meta-analysis on the estimated within-district ICCs. Our analysis is performed by grade and subject for different strata designated by district size (number of schools), urbanicity, and poverty rates.

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. Objectives: 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. Research Design: 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.

Background: Policy makers and researchers are frequently interested in understanding how effective a particular intervention may be for a specific population. One approach is to assess the degree of similarity between the sample in an experiment and the population. Another approach is to combine information from the experiment and the population to estimate the population average treatment effect (PATE). Method: Several methods for assessing the similarity between a sample and population currently exist as well as methods estimating the PATE. In this article, we investigate properties of six of these methods and statistics in the small sample sizes common in education research (i.e., 10–70 sites), evaluating the utility of rules of thumb developed from observational studies in the generalization case. Result: In small random samples, large differences between the sample and population can arise simply by chance and many of the statistics commonly used in generalization are a function of both sample size and the number of covariates being compared. The rules of thumb developed in observational studies (which are commonly applied in generalization) are much too conservative given the small sample sizes found in generalization. Conclusion: This article implies that sharp inferences to large populations from small experiments are difficult even with probability sampling. Features of random samples should be kept in mind when evaluating the extent to which results from experiments conducted on nonrandom samples might generalize.

This text provides a concise and clearly presented discussion of all the elements in a meta-analysis. It is illustrated with worked examples throughout, with visual explanations, using screenshots from Excel spreadsheets and computer programs such as Comprehensive Meta-Analysis (CMA) or Strata