Cluster Sampling Design Effect Calculator
Compute the design effect (DEFF) and effective sample size for a cluster survey from cluster size and intra-cluster correlation.
How it works
DEFF = 1 + (m − 1)·ρ · effective n = nominal n ÷ DEFF · DEFT = √DEFF
Cluster sampling — interviewing several people in each of many villages, schools or households — is cheaper than a simple random sample but less efficient, because people in the same cluster tend to be alike. Kish's design effect quantifies that loss: it multiplies the variance you would get from simple random sampling. The effective sample size divides your nominal size by the design effect, telling you how many truly independent observations your survey is worth.
Worked example
With 20 interviews per cluster and an intra-cluster correlation of 0.05: DEFF = 1 + (20−1)·0.05 = 1.95. A nominal 600 interviews then carry the precision of only 600 ÷ 1.95 ≈ 308 independent observations.
Sources: Design effect — Wikipedia
Frequently asked questions
What is a typical intra-cluster correlation?
It depends on the outcome and the clustering. Attitudes measured within neighbourhoods often show ρ around 0.01–0.10, while highly localised traits can run higher. Even a small ρ has a large effect when clusters are big.
How do I use the design effect when planning?
Multiply the simple-random sample size you would otherwise need by the design effect to get the clustered sample size. This "sample needed to match SRS" figure keeps your precision intact despite the clustering.
Does a smaller cluster size help?
Yes. Because DEFF grows with (m − 1), interviewing fewer people in more clusters lowers the design effect for the same total sample — at the cost of visiting more locations.
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This calculator is for educational purposes. Double-check important results before acting on them.