Cluster-Randomized Experiments
When an intervention is delivered to a tutorial section, school, team, clinic, or community—or when spillovers make individual assignment implausible—the cluster may be the honest assignment unit. Cluster randomization answers a policy question about assigning whole groups, not the same question as assigning isolated individuals.
Prerequisites
Complete Power, Minimum Effect, and Sample Size. Distinguish assignment units from observation units.
Learning goals
- Explain how within-cluster similarity reduces independent information.
- Plan allocation, recruitment, power, and analysis around clusters.
- Identify cluster-specific consent, interference, and selection risks.
Why 300 students are not 300 independent assignments
Students in one tutorial section share teaching, peers, and context. The intracluster correlation (ICC), , summarizes outcome similarity within clusters under a working model. For equal cluster size , the simple design effect is
clusters = 20
mean_size = 15
icc = 0.08
observations = clusters * mean_size
design_effect = 1 + (mean_size - 1) * icc
effective_n = observations / design_effect
print(f"clusters={clusters} mean size={mean_size} ICC={icc:.2f}")
print(f"design effect={design_effect:.2f} effective n={effective_n:.1f}")
The effective-size calculation is an intuition aid, not the final power analysis. Unequal sizes usually cost more information; few clusters make asymptotic standard errors unreliable; ICC uncertainty deserves sensitivity analysis. Adding members to an existing cluster often contributes less information than adding another cluster.
Design implications
Define clusters before assignment, recruit enough clusters in each arm, and consider stratifying or pairing clusters on strong pre-treatment predictors. Record whether individuals are identified and consented before or after cluster assignment. Recruiting people after their cluster's condition is known can create differential selection.
Interference within clusters may be part of the policy treatment, while spillovers between clusters threaten separation. State cluster boundaries, expected cross-cluster contact, treatment delivery, and whether the estimand is an offer effect for all eligible members or only enrolled participants.
Analysis implications
The unit of analysis must respect the assignment structure. With enough clusters, use a prespecified mixed model, generalized estimating equation, randomization-based method, or regression with cluster-robust standard errors suited to the design and number of clusters. With few clusters, small-sample corrections or randomization inference may be necessary. A simpler option is to analyze at the cluster level, comparing cluster summaries while reflecting stratification or pairing.
Do not run an ordinary student-level test that assumes independent residuals. Report cluster counts, sizes, ICC assumptions and estimates, losses by arm, and whether analysis weights make the estimand student-weighted or cluster-weighted.
Ethics and consent
A gatekeeper may authorize access to a cluster but cannot automatically provide individual informed consent for every member or waive privacy obligations. Some interventions cannot be declined at the individual level; make that exposure explicit, minimize risk, and obtain appropriate local review. This page is design education, not medical or legal approval guidance.
Common mistakes
- Inflating a student-level sample size while leaving too few clusters for credible inference.
- Assigning clusters but analyzing students as independent.
- Ignoring variable cluster sizes or post-assignment recruitment.
- Assuming clustering eliminates interference between clusters.
- Confusing a cluster-policy estimand with an individually delivered treatment effect.
Practice
Redesign Study Sprint with tutorial sections as clusters. Specify eligibility timing, number of clusters per arm, size distribution, ICC range, stratification, consent path, spillover boundary, analysis method, and whether the target averages equally over students or sections.
Next steps
Factorial Experiments uses randomization to study two intervention components and their interaction in one design.
Primary sources
Checked 2026-10-15: CONSORT 2010 extension to cluster randomized trials, Donner and Klar, “Pitfalls of and Controversies in Cluster Randomization Trials”, and The Belmont Report.