Cluster Randomised Controlled Trial Sample Size Calculator

Plan cluster studies with design effect adjustments. Test balanced allocations for binary or continuous outcomes. See clusters, participants, attrition needs, and sensitivity charts instantly.

Calculator Inputs

Choose an outcome type, enter trial assumptions, then calculate participants and clusters for each arm.

This planner uses normal approximation formulas and a design effect adjustment. Final protocols may still need simulation, specialist review, and sensitivity checks.

Example Data Table

Scenario Outcome Alpha Power Avg Cluster Size ICC Cluster CV Attrition Key Inputs
Community prevention trial Binary 0.05 0.80 18 0.02 0.15 8% Control 0.30, Intervention 0.20, Ratio 1.00
School attendance study Continuous 0.05 0.90 25 0.05 0.25 12% Mean difference 3.50, SD 9.00, Ratio 1.00
Primary care service trial Binary 0.025 0.85 30 0.04 0.30 10% Control 0.40, Intervention 0.28, Ratio 1.50

Formula Used

Design effect with unequal cluster size:
DE = 1 + [((CV² + 1) × m) − 1] × ICC
Here, m is average cluster size, CV is the cluster size coefficient of variation, and ICC is the intracluster correlation.
Continuous outcome, control arm individual sample:
ncontrol = (Zα + Zβ)² × σ² × (1 + 1/r) / Δ²
σ is common standard deviation, Δ is the absolute mean difference, and r is intervention/control allocation ratio.
Binary outcome, control arm individual sample:
ncontrol = [ Zα × √((1 + 1/r) × p̄ × (1 − p̄)) + Zβ × √(p1 × (1 − p1) + p2 × (1 − p2)/r) ]² / (p1 − p2)²
p̄ = (p1 + r × p2) / (1 + r), where p1 is control risk and p2 is intervention risk.
Cluster adjusted requirements:
Analysed participants per arm = Individual sample × DE
Recruited participants per arm = Analysed participants / (1 − attrition)
Clusters per arm = Ceiling(Recruited participants / m)

How to Use This Calculator

  1. Select either continuous or binary outcome mode.
  2. Choose one-sided or two-sided testing.
  3. Enter alpha, power, and allocation ratio.
  4. Enter average cluster size, ICC, cluster size CV, and attrition.
  5. Add either mean difference and standard deviation, or event proportions.
  6. Click calculate to view analysed counts, recruited counts, and clusters per arm.
  7. Review the sensitivity chart to see how ICC changes cluster demand.
  8. Download CSV or PDF files for protocol drafts or team review.

Frequently Asked Questions

1) What is a cluster randomised controlled trial?

It randomises groups rather than individuals. Examples include schools, clinics, wards, practices, or communities. Sample size must account for correlation inside each cluster.

2) Why does ICC matter so much?

ICC measures how similar participants are within the same cluster. Higher ICC increases the design effect, which increases the required number of participants and clusters.

3) What does cluster size CV change?

CV captures unequal cluster sizes. When cluster sizes vary more, efficiency falls. The calculator increases the design effect to reflect that loss.

4) When should I use binary versus continuous mode?

Use binary mode for event proportions, such as success or failure. Use continuous mode for averages, such as scores, blood pressure, or attendance days.

5) Why are clusters rounded up?

You cannot recruit a fraction of a cluster. The calculator rounds clusters upward, then reports actual recruits implied by whole clusters.

6) How is attrition handled here?

Attrition inflates recruitment targets after clustering adjustment. The tool divides required analysed participants by the expected retention proportion.

7) Can I use unequal allocation?

Yes. Enter the intervention-to-control ratio. Ratios above one assign more participants to intervention, and ratios below one assign fewer.

8) When is simulation a better choice?

Simulation is better for complex designs, strong baseline adjustment, stepped rollouts, few clusters, nonstandard outcomes, or uncertain ICC distributions.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.