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Cluster Sample Design Effect Calculator

Work out cluster sample design effect instantly with clear inputs, formula shown and shareable results.

About Cluster Sample Design Effect Calculator

Cluster sampling loses efficiency because people within a cluster resemble each other. The design effect is 1 + (m-1)ICC, so clusters of 25 with an ICC of 0.05 give 2.2 - meaning 400 participants under simple random sampling becomes 880, spread across 36 clusters. Even a small ICC is costly when clusters are large.

Formulas

Design effect

DEFF = 1 + (cluster size - 1) x ICC

Adjusted sample

adjusted = simple random sample x design effect

Worked example

With the default values below, Cluster Sample Design Effect Calculator returns Design Effect of 2.2000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Average cluster sizeminimum 1
25
Intracluster correlationaccepts 0–1
0.05
Sample needed under simple random samplingminimum 1
400

Results

Design Effect
2.2000
Sample Size Required
880
Clusters Required
36
Effective Sample Size
400

Step by step

  1. 1Values used
  2. 2Design effect
  3. 3Adjusted sample
  4. 4Design Effect= 2.2000
  5. 5Sample Size Required= 880
  6. 6Clusters Required= 36
  7. 7Effective Sample Size= 400

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does a tiny ICC matter so much?

Because it is multiplied by cluster size. An ICC of 0.02 with clusters of 100 still gives a design effect near 3.

Is it better to have more clusters or bigger ones?

More clusters, almost always. Adding participants within a cluster adds little new information once the cluster mean is estimated.

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