Causal effects are commonly defined as comparisons of the potential outcomes under treatment and control, but this definition is threatened by the possibility that either the treatment or the control condition is not well defined, existing instead in more than one version. This is often a real possibility in nonexperimental or observational…

For RCTs of education interventions, it is often of interest to estimate associations between student and mediating teacher practice outcomes, to examine the extent to which the study's conceptual model is supported by the data, and to identify specific mediators that are most associated with student learning. This article develops statistical…

When estimating causal effects from observational data, it is desirable to approximate a randomized experiment as closely as possible. This goal can often be achieved by choosing a subsample from the original control group that matches the treatment group on the distribution of the observed covariates. However, sometimes the original control group…