The Impact of Covariates on Statistical Power in Cluster Randomized Designs: Which Level Matters More?

Field experiments with nested structures are becoming increasingly common, especially designs that assign randomly entire clusters such as schools to a treatment and a control group. In such large-scale cluster randomized studies the challenge is to obtain sufficient power of the test of the treatment effect. The objective is to maximize power without adding many clusters that make the study much more expensive. In this article I discuss how power estimates of tests of treatment effects in balanced cluster randomized designs are affected by covariates at different levels. I use third-grade data from Project STAR, a field experiment about class size, to demonstrate how covariates that explain a considerable proportion of variance in outcomes increase power significantly. When lower level covariates are group-mean centered and clustering effects are larger, top-level covariates increase power more than lower level covariates. In contrast, when clustering effects are smaller and lower level covariates are grand-mean centered or uncentered, lower level covariates increase power more than top-level covariates.