Fig. 5

Power of multilevel analysis to detect the overall experimental effect in research design B. Power is depicted in nine conditions (effect size d of 0.20, 0.50, or 0.80, and cluster-related variation in the experimental effect of 0.00, 0.05, and 0.15) and as function of the number of clusters (a) or the number of observations per cluster per condition (b). In both a and b, two experimental conditions are compared, using a balanced research design. As the cluster-related variation in the intercept in research design B does not influence the statistical power to detect the overall experimental effect (see Eq. 8 in “Box 3”), the ICC does not feature in this figure. In a, the number of observations is held constant at 5 observations per condition in each cluster; in b, the number of clusters is held constant at 10. Evidently, the number of clusters, and not the number of observations per cluster, is essential to increase the statistical power to detect the experimental effect