Estimating the Standard Error of the Impact Estimator in Individually Randomized Trials with Clustering
In many experimental evaluations in the social and medical sciences, individuals are randomly assigned to a treatment arm or a control arm of the experiment. After treatment assignment is determined, individuals within one or both experimental arms are frequently grouped together (e.g., within classrooms or schools, through shared case managers, in group therapy sessions, or through shared doctors) to receive services. Consequently, there may be within-group correlations in outcomes resulting from (1) the process that sorts individuals into groups, (2) service provider effects, and/or (3) peer effects. When estimating the standard error of the impact estimate, it may be necessary to account for within-group correlations in outcomes. This article demonstrates that correlations in outcomes arising from nonrandom sorting of individuals into groups leads to bias in the estimated standard error of the impact estimator reported by common estimation approaches.