A linear model is often used to find the effect of a binary treatment D on a noncontinuous outcome Y with covariates X. Particularly, a binary Y gives the popular "linear probability model (LPM)," but the linear model is untenable if X contains a continuous regressor. This raises the question: what kind of treatment effect does the…

Recent methods have sought to improve precision in randomized controlled trials (RCTs) by utilizing data from large observational datasets for covariate adjustment. For example, consider an RCT aimed at evaluating a new algebra curriculum, in which a few dozen schools are randomly assigned to treatment (new curriculum) or control (standard…

A major obstacle to developing evidenced-based policy is the difficulty of implementing randomized experiments to answer all causal questions of interest. When using a nonexperimental study, it is critical to assess how much the results could be affected by unmeasured confounding. We present a set of graphical and numeric tools to explore the…