Estimating effect size when there is clustering in one treatment group

Abstract

Some experimental designs involve clustering within only one treatment group. Such designs may involve group tutoring, therapy administered by multiple therapists, or interventions administered by clinics for the treatment group, whereas the control group receives no treatment. In such cases, the data analysis often proceeds as if there were no clustering within the treatment group. A consequence is that the actual significance level of the treatment effects is larger (i.e., actual p values are larger) than nominal. Additionally, biases will be introduced in estimates of the effect sizes and their variances, leading to inflated effects and underestimated variances when clustering in the treatment group is not taken into account. These consequences of clustering can seriously compromise the interpretation of study results. This article shows how information on the intraclass correlation can be used to obtain a correction for biases in the effect sizes and their variances, and also to obtain an adjustment to the significance test for the effects of clustering.