Estimators for Clustered Education RCTs Using the Neyman Model for Causal Inference

Abstract

This article examines the estimation of two-stage clustered designs for education randomized control trials (RCTs) using the nonparametric Neyman causal inference framework that underlies experiments. The key distinction between the considered causal models is whether potential treatment and control group outcomes are considered to be fixed for the study population (the finite-population model) or randomly selected from a vaguely defined universe (the super-population model). Both approaches allow for heterogeneity of treatment effects. Appropriate estimation methods and asymptotic moments are discussed for each model using simple differences-in-means estimators and those that include baseline covariates. An empirical application using a large-scale education RCT shows that the choice of the finite- or super-population approach can matter. Thus, the choice of framework and sensitivity analyses should be specified and justified in the analysis protocols.