Clinical Trial Designs · Cluster-Randomized Trials

Cluster-Randomized Superiority Trial — Continuous Outcome

Plan a one-sided superiority comparison between experimental and reference arms with a continuous primary outcome.

How this calculator works

The treatment contrast is experimental minus reference. The calculator tests the prespecified one-sided superiority hypothesis using a cluster-level noncentral-t planning approximation and searches whole-cluster allocations.

Use this calculator only when the direction of benefit is justified before the trial begins. Use a two-sided general comparison when either direction would constitute a relevant difference.

1. Planning setup

Primary outcome name

Optional. Used only in the protocol-ready wording and calculation summary.

Cluster-size assumption

EqualVariable

Choose variable when retained clusters are expected to contribute meaningfully different numbers of analysable participants.

2. Information obtained from previous study / literature

Expected common outcome SD σ

Use the expected individual-level standard deviation of the continuous primary outcome.

Intracluster correlation coefficient ρ

Use evidence from a comparable outcome, population and clustering unit.

Analysable mean participants per retained cluster m

Enter the mean number expected to contribute analysable primary-outcome data in each retained cluster.

3. Information decided by the researcher

Minimum clinically important mean difference Δ

Enter the smallest absolute between-arm difference the study should be able to detect.

Superiority hypothesis

One-sided: the prespecified favourable group 2 mean is superior to group 1. Use the general two-mean calculator for a non-directional equality-null test.

One-sided significance level α

Enter the prespecified one-sided Type I error rate.

Statistical power

Group 2:group 1 cluster allocation ratio

Enter 1 for equal allocation, 2 for 1:2, or 0.5 for 2:1.

Participant-level attrition

Inflates participants per recruited cluster without changing the analysable cluster requirement.

Whole-cluster attrition

Inflates the number of randomized clusters separately in each arm.

4. Results

Enter the cluster-trial assumptions and select Calculate.

Allocation and recruitment

Arm	Analysable clusters	Analysable participants	Recruit clusters	Recruit participants

ICC sensitivity analysis

ICC	Design effect	Group 1 clusters	Group 2 clusters	Total clusters

Choose the planning ICC from credible external evidence; do not select an ICC merely because it gives a convenient sample size.

Suggested sample-size wording

Formula, assumptions, limitations, and methodological note

Example clinical scenario

Primary-care clinics are randomized to an implementation programme or usual care, and mean systolic blood pressure is compared between arms at six months.

Formula and methodological note

The calculator uses a cluster-level noncentral-t planning approximation. For equal cluster sizes, the design effect is 1 + (m − 1)ρ. Variable-size mode uses 1 + ([(1 + CV²)m] − 1)ρ. Candidate integer cluster allocations are evaluated with df = k1 + k2 − 2.

It assumes two independent arms, a common SD, common ICC and common analysable mean cluster size. The CV adjustment is a planning approximation. It excludes matched, stratified, multilevel, stepped-wedge, repeated-outcome, non-inferiority and simulation-based designs. The final analysis must account for clustering and should use an appropriate small-sample correction when clusters are few.

This tool supports research planning and does not replace protocol-specific statistical consultation.

Technical results

Method references

Campbell MK, Piaggio G, Elbourne DR, Altman DG. CONSORT 2010 statement: extension to cluster randomised trials. BMJ. 2012;345:e5661.
Eldridge SM, Ashby D, Kerry S. Sample size for cluster randomized trials: effect of coefficient of variation of cluster size and analysis method. Int J Epidemiol. 2006;35:1292–1300.

Privacy: Calculations run locally in your browser. Values entered are not uploaded by this calculator.

Planning disclaimer: This tool supports research planning and does not replace protocol-specific statistical consultation.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for a Cluster-Randomized Superiority Trial — Continuous Outcome (CRT-2A-C).” Web calculator. NajibMY, 2026. Accessed August 5, 2026. http://127.0.0.1:4321/tools/sample-size/clinical-complex-study-designs/parallel-cluster-randomized-continuous-outcome/.