Compute the design effect (also called Variance Inflation Factor) for mixed models with two-level design.

design_effect(n, icc = 0.05)



Average number of observations per grouping cluster (i.e. level-2 unit).


Assumed intraclass correlation coefficient for multilevel-model.


The design effect (Variance Inflation Factor) for the two-level model.


The formula for the design effect is simply (1 + (n - 1) * icc).


Bland JM. 2000. Sample size in guidelines trials. Fam Pract. (17), 17-20.

Hsieh FY, Lavori PW, Cohen HJ, Feussner JR. 2003. An Overview of Variance Inflation Factors for Sample-Size Calculation. Evaluation and the Health Professions 26: 239-257. doi: 10.1177/0163278703255230

Snijders TAB. 2005. Power and Sample Size in Multilevel Linear Models. In: Everitt BS, Howell DC (Hrsg.). Encyclopedia of Statistics in Behavioral Science. Chichester, UK: John Wiley and Sons, Ltd. doi: 10.1002/0470013192.bsa492

Thompson DM, Fernald DH, Mold JW. 2012. Intraclass Correlation Coefficients Typical of Cluster-Randomized Studies: Estimates From the Robert Wood Johnson Prescription for Health Projects. The Annals of Family Medicine;10(3):235-40. doi: 10.1370/afm.1347


# Design effect for two-level model with 30 observations per
# cluster group (level-2 unit) and an assumed intraclass
# correlation coefficient of 0.05.
design_effect(n = 30)
#> [1] 2.45

# Design effect for two-level model with 24 observation per cluster
# group and an assumed intraclass correlation coefficient of 0.2.
design_effect(n = 24, icc = 0.2)
#> [1] 5.6