TABLE 1—

Two Common Measures of Clustering for General Clustered Data for Two Common Types of Outcome

Outcome Measure	ICC, ρa	CV, k	Relationship of ICC to CVb
Continuous
Binary

Note. CV = coefficient of variation; GRT = group-randomized trial; ICC = intraclass correlation coefficient. μ is the overall mean for continuous outcome data; π is the overall proportion for binary outcome data; is the between-group variance; is the within-group variance (i.e., residual error variance). As is common practice, the 2 clustering measures are for general clustered data and do not focus on the GRT design in which the intervention effect is of primary interest (chapter 2 of Hayes and Moulton,² e.g., provides more detail). The intervention parameter of interest in GRTs is typically the following: difference of means for continuous outcomes; difference of proportions; ratio of proportions or odds ratio for binary outcomes; or rate difference or rate ratio for event outcomes.

^aThere are multiple definitions of the ICC for binary outcomes.^12–17 The specific formulation we have provided is 1 of the simplest and most commonly used (e.g., Equation 2.4 of Hayes and Moulton² and Equation 8 of Eldridge et al.⁹).

^bNote that whereas the relationship for binary outcomes is only a function of k and the distributional parameter of interest, π, the relationship for continuous outcomes is a function of both the distributional parameter of interest, μ, and .