A Valid Analysis of a Small Subsample: The Case of Non-Citizen Registration and Voting

The development of large sample surveys creates new opportunities for analysis of subpopulations that would hitherto have been impossible to examine systematically. But it also raises key challenges. Low level measurement error can potentially lead to substantial biases in estimates drawn from small subsamples. This study details strategies researchers may take to make inferences in the context of this subsample-response-error problem. In the non-citizen voting case, which recently has received substantial attention, we show that attention to any of these strategies -group-specific response error estimates, correlated higher-frequency events, test-retest validity, or analysis of associated hypotheses – produces significant evidence that non-citizens participated in recent US elections. It is also important that researchers aiming to debunk a study using this argument have a test with sufficient power. The analysis reaffirms the validity of the core claim made by Richman, Chattha, and Earnest (2014): a small percentage of non-citizens vote in US elections.