I wanted to look into the case where you have an experiment in which your units of analysis are naturally clustered (e.g., households in villages), but you randomize *within* clusters. The goal is to estimate a treatment effect in terms of difference in means, using design-based principles and frequentist methods for inference.

Randomization ensures that the difference in means is unbiased for the sample average treatment effect. Using only randomization as the basis for inference, I know the variance of this estimator is *not* identified for the sample, as it requires knowledge of the covariance of potential outcomes. But the usual sample estimators for the variance are conservative. If, however, the experiment is run on a random sample from an infinitely large population, then the standard methods are unbiased for the mean and for the variance of the difference in means estimator applied to this population (refer to Neyman, 1990; Rubin, 1990; Imai, 2008; for finite populations, things are more complicated, and the infinite population assumption is often a reasonable approximation). I understand that these are the principles that justify the usual frequentist estimation techniques for inference on population level treatment effects in randomized experiments.

The question I had was, how should we account for dependencies in potential outcomes within clusters? Continue reading “Clustering, unit level randomization, and inference (updated, Nov 5)”