In the previous article, we discussed the clustering effects when data in clusters such as several teeth nested within patient clusters are correlated. We also introduced the intracluster correlation coefficient (ICC) and the coefficient of variation ( *cv* or *k* ), which indicate the degree of similarity of observations within clusters or heterogeneity between clusters. Finally, we explained that, with clustering effects, there is power loss; thus, sample sizes must be revised upward to compensate for this effect. The design effect formula was introduced that incorporates the ICC and indicates how much we must increase the required sample size of a trial with clustering effects and in comparison with a trial without clustering effects.

This formula gives the design effect, where *m* is the number of units per cluster, such as number of teeth per patient, and *ρ* is the ICC.

Clustering effects are important to orthodontic research because they are often encountered when individual teeth constitute the unit at which the intervention is applied or when repeated measurements are conducted on each patient. For example, clustering effects arise when assessing bracket bond failures, bilateral canine impactions, and pain scores over periods of time. Authors of a recent study found that clustering effects in orthodontic research are often ignored.

Next, we will perform sample calculations for clustered designs following the same procedures as in the previous articles on sample size of this series. The formulas used for sample calculations or proportions and mean differences can be adapted by incorporating the coefficient of variation when calculating sample sizes for cluster randomized trials.

c = 1 + f ( α , β ) χ π 1 ( 1 − π 1 ) / m + π 2 ( 1 − π 2 ) / + k 2 ( π 1 2 + π 2 2 ) ( π 1 − π 2 ) 2