ICC in the multilevel model (share of the groups)

The ICC (intraclass correlation) in the multilevel model is the share of the total variation that lies between the groups: variance between groups divided by the sum of the variance between and within groups, calculated in the model without explanatory columns (null model). An ICC of .16 means 16% of the differences are due to the group. The design effect = 1 + (mean group size − 1) · ICC shows by what factor the variance of a mean is larger than expected for independent cases.

Example: ICC = .16 with 18 cases per group: design effect = 1 + 17 · .16 = 3.7. The standard errors of an analysis that ignores the groups would be too small by about a factor of 1.9.

Caution: Not to be confused with the ICC of agreement between raters (question "Do ratings agree?"): the one here is the share of the groups in the variation, there it is the agreement of ratings. Rule of thumb for size: from .05 small, from .10 medium, from .15 large (Hox).