Clustered Samples and Assuming Independence of Observations

I sometimes speak to researchers who have a design where units are nested within clusters (e.g., 200 employees nested within 50 stores). While this is often called cluster sampling, the research that this post addresses is often more about convenience than about following a rigorous sampling plan. At some point, the researchers discover that this clustering has implications for the assumption of independence of observations, which in turn has implications for the validity of standard statistical techniques, such as t-tests and regressions that assume independence. This post discusses what to do in such a situation and when if ever it is appropriate to ignore the clustered nature of the sampling.