Using robust standard errors for the analysis of binary outcomes with a small number of clusters


Binary outcomes are often analyzed in cluster randomized trials (CRTs) using logistic regression and cluster robust standard errors (CRSEs) are routinely used to account for the dependent nature of nested data in such models. However, CRSEs can be problematic when the number of clusters is low (e.g., < 50) and with CRTs, a low number of clusters is quite common. We investigate the use of the CR2 CRSE and an empirical degrees of freedom adjustment (dofBM) proposed by Bell and McCaffrey (2002) with a simulation using binary outcomes and illustrate its use with an applied example. Findings show that the CR2 (w/dofBM) standard errors are relatively unbiased with coverage and power rates for group-level predictors that are comparable to that of a multilevel logistic regression model and can be used even with as few as 10 clusters. To promote its use, a free graphical SPSS extension is provided that can fit logistic (and linear) regression models with a variety of CRSEs and dof adjustments (available at

Journal of Research on Educational Effectiveness.

All code for replicating the simulation and the applied example are available at The CR2 package is also available on CRAN: install.packages("CR2").