Calculator Inputs
Choose an outcome type, enter trial assumptions, then calculate participants and clusters for each arm.
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
DE = 1 + [((CV² + 1) × m) − 1] × ICCHere,
m is average cluster size, CV is the cluster size coefficient of variation, and ICC is the intracluster correlation.
ncontrol = (Zα + Zβ)² × σ² × (1 + 1/r) / Δ²σ is common standard deviation, Δ is the absolute mean difference, and r is intervention/control allocation ratio.
ncontrol = [ Zα × √((1 + 1/r) × p̄ × (1 − p̄)) + Zβ × √(p1 × (1 − p1) + p2 × (1 − p2)/r) ]² / (p1 − p2)²p̄ = (p1 + r × p2) / (1 + r), where p1 is control risk and p2 is intervention risk.
Analysed participants per arm = Individual sample × DERecruited participants per arm = Analysed participants / (1 − attrition)Clusters per arm = Ceiling(Recruited participants / m)
How to Use This Calculator
- Select either continuous or binary outcome mode.
- Choose one-sided or two-sided testing.
- Enter alpha, power, and allocation ratio.
- Enter average cluster size, ICC, cluster size CV, and attrition.
- Add either mean difference and standard deviation, or event proportions.
- Click calculate to view analysed counts, recruited counts, and clusters per arm.
- Review the sensitivity chart to see how ICC changes cluster demand.
- 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.