Calculate cluster counts, average members, and expected sample size. Compare coverage, response rate, and totals. Build reliable grouped studies using simple inputs and exports.
For one-stage cluster sampling, set units sampled per selected cluster equal to the average cluster size.
This calculator helps plan cluster random sampling studies by combining population structure, sampled clusters, expected response, and intracluster correlation. It estimates how much useful information your design may produce, because clustered data often contain less independent information than a simple random sample of the same raw size.
The tool is useful for survey planning, field audits, classroom studies, health screening programs, village sampling, household studies, and any grouped population where random selection happens by cluster first and by element second. It also shows a quick precision check through design effect, effective sample size, and achieved margin of error.
1) Total population units
Total Population = Total Clusters × Average Units per Cluster
2) Gross sampled units
Gross Sample = Selected Clusters × Units Sampled per Selected Cluster
3) Expected completed units
Expected Completed = Gross Sample × Response Rate
4) Simple random sample estimate
n₀ = z² × p × (1 - p) / e²
5) Finite population adjustment
n = (N × n₀) / ((N - 1) + n₀)
6) Design effect for clustering
DEFF = 1 + (m - 1) × ρ
7) Cluster-adjusted required completed sample
Required Completed = n × DEFF
8) Effective sample size
Effective Sample = Expected Completed / DEFF
9) Approximate achieved margin of error
MOE = z × √Variance
Here, z is the confidence multiplier, p is the estimated proportion, e is the target margin of error, m is sampled units per selected cluster, and ρ is the intracluster correlation.
| Cluster ID | Cluster Size | Selected | Units Sampled | Completed Units |
|---|---|---|---|---|
| C-01 | 42 | No | 0 | 0 |
| C-02 | 47 | Yes | 20 | 18 |
| C-03 | 44 | No | 0 | 0 |
| C-04 | 46 | Yes | 20 | 19 |
| C-05 | 43 | Yes | 20 | 18 |
This example shows a grouped population where only selected clusters contribute sampled and completed units.
It estimates population units, sampled units, expected completes, design effect, effective sample size, variance, achieved margin of error, sampling weights, and recommended clusters.
Higher intracluster correlation means units inside a cluster look more alike. That raises design effect and usually increases the number of clusters needed for the same precision.
Use equal values for one-stage cluster sampling, where every unit in each selected cluster is observed. Use a smaller value for two-stage designs.
Yes. Lower response rates reduce completed observations. The calculator increases gross sample needs and recommended clusters so expected completed cases still support target precision.
It is the completed sample adjusted for clustering. Two studies with the same raw sample may produce different precision if their design effects differ.
Yes, but extreme proportions reduce variance. If you lack a prior estimate, using 50 percent is conservative because it produces the largest required sample size.
No. It is an approximation based on average cluster size. Strongly unequal clusters may require weighting, specialized variance estimation, and deeper design planning.
Your target precision may be unrealistic under current assumptions. Increase sampled units, relax margin of error, improve response rate, or reconsider the cluster design.
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.