  This article develops design-based ratio estimators for clustered, blocked
randomized controlled trials (RCTs), with an application to a federally funded,
school-based RCT testing the effects of behavioral health interventions. We
consider finite population weighted least squares estimators for average
treatment effects (ATEs), allowing for general weighting schemes and
covariates. We consider models with block-by-treatment status interactions as
well as restricted models with block indicators only. We prove new finite
population central limit theorems for each block specification. We also discuss
simple variance estimators that share features with commonly used
cluster-robust standard error estimators. Simulations show that the
design-based ATE estimator yields nominal rejection rates with standard errors
near true ones, even with few clusters.
