Sampling Frame Calculator
Calculate the design effect and effective sample size for cluster sampling designs. Understand how intraclass correlation and cluster size reduce your statistical power.
About this calculator
This calculator estimates the Design Effect (DEFF) of a cluster sampling design and the loss of statistical precision it causes, using Kish's classic formula, published in his 1965 book "Survey Sampling": Design Effect = 1 + (Average Cluster Size − 1) × Intraclass Correlation (line 10). Raising either Average Cluster Size or ICC pushes Design Effect above 1, which shrinks Effective Sample Size = Total Sample Size ÷ Design Effect (line 13) — the sample size an unclustered simple random sample would need to match your clustered design's precision. Total Sample Size is the dominant driver of Effective Sample Size, since it's the numerator and is itself unaffected by clustering.
Number of Clusters, despite being one of the four listed inputs, plays no role in any of these calculations at all — reading the full function shows its only use is being echoed straight back as Total Clusters (line 43); it never feeds into Design Effect, Effective Sample Size, or Effective Clusters. This calculator does not account for unequal cluster sizes: Kish's formula assumes every cluster contains exactly Average Cluster Size individuals, so a real design with a few very large clusters and many small ones will have its true design effect misestimated by this single average-based formula.
Inputs
Results
Design Effect (DEFF)
1.95
Figures current as of 1965. Source: Kish, L. (1965). Survey Sampling. New York: John Wiley & Sons.
How to Use This Calculator
- Enter your total sample size and the number of clusters in your sampling design.
- Input the intraclass correlation (ICC) and the average cluster size.
- Review the Design Effect (DEFF) and Effective Sample Size results.
- Check the SRS-Equivalent Sample and Efficiency Loss to see how much clustering reduces your statistical power.
- Use the Design Effect by ICC chart to see how sensitivity changes with different ICC values.
How the result changes with Average Cluster Size
| Average Cluster Size | Design Effect (DEFF) |
|---|---|
| 10 | 1.45 |
| 15 | 1.7 |
| 30 | 2.45 |
| 50 | 3.45 |
What each input means
- Total Sample Size
- The total number of individual observations in your sample across all clusters.
- Number of Clusters
- The number of clusters (e.g., schools, clinics, neighborhoods) in your sampling design.
- Intraclass Correlation (ICC)
- The ICC measures similarity within clusters. Values of 0.01-0.05 are common in social research; 0.1-0.3 in educational or health research.
- Average Cluster Size
- Average number of individuals sampled per cluster. Equals total sample size / number of clusters.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersTotal Sample Size = 1000, Number of Clusters = 50, Intraclass Correlation (ICC) = 0.05, Average Cluster Size = 20 = 4 input(s) provided
- Calculate Design EffectDesign Effect1.95 = 1.95
- Calculate Effective Sample Size513 = 513
- Calculate SRS-Equivalent SampleSRS-Equivalent Sample513 = 513
Figures and sources
- Kish's design effect for cluster sampling (Deff = 1 + (avg cluster size − 1) × ICC) (1965) — Kish, L. (1965). Survey Sampling. New York: John Wiley & Sons.
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Does the Number of Clusters field change the Design Effect or Effective Sample Size?
No. Despite sitting alongside the other three inputs, Number of Clusters is only ever used to echo back Total Clusters (line 43) — Design Effect, Effective Sample Size, and Effective Clusters are all computed from Total Sample Size, ICC, and Average Cluster Size instead, and never reference Number of Clusters.
Why do Design Effect and Variance Inflation always show the same number?
Because they are the same number under the hood — the engine sets varianceInflation equal to designEffect directly with no separate formula of its own (line 16), so the two outputs will always move together identically no matter which input you adjust.
Which input has the biggest effect on Effective Clusters?
Average Cluster Size, because it appears twice in the calculation chain: once inside the Design Effect formula and again as the direct divisor that converts Effective Sample Size into Effective Clusters, giving it a larger combined influence than Total Sample Size, which only enters once.
What does a Design Effect greater than 1 mean for my survey?
It means clustering has cost you statistical precision. Since Design Effect = 1 + (Average Cluster Size − 1) × ICC (line 10) — the formula statistician Leslie Kish published in his 1965 book "Survey Sampling" — any positive ICC with more than one person per cluster pushes it above 1, and Effective Sample Size will end up smaller than the number of people you actually surveyed.
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