Many generalization studies in education are typically based on a sample of 30-70 schools while the inference population is at least twenty times larger. This small sample to population size ratio limits the precision of design-based estimators of the population average treatment effect. Prior work has shown the potential of small area estimation…

The main result of an experiment is typically an estimate of the average treatment effect (ATE) and its standard error. In most experiments, the number of covariates that may be moderators is large. One way this issue is typically skirted is by interpreting the ATE as the average effect for "some" population. Cornfield and Tukey (1956)…

As a result of the use of random assignment to treatment, randomized experiments typically have high internal validity. However, units are very rarely randomly selected from a well-defined population of interest into an experiment; this results in low external validity. Under nonrandom sampling, this means that the estimate of the sample average…