Applied Statistics Commons^™

Asymptotic Behavior Of A T Test Robust To Cluster Heterogeneity, Douglas G. Steigerwald

Douglas G. Steigerwald

We study the behavior of a cluster-robust t statistic and make two principle contributions. First, we relax the restriction of previous asymptotic theory that clusters have identical size, and establish that the cluster-robust t statistic continues to have a Gaussian asymptotic null distribution. Second, we determine how variation in cluster sizes, together with other sources of cluster heterogeneity, affect the behavior of the test statistic. To do so, we determine the sample specific measure of cluster heterogeneity that governs this behavior and show that the measure depends on how three quantities vary over clusters: cluster size, the cluster specific error …