Calculator form
Plotly graph
The chart shows how total design effect changes as ICC rises for smaller, current, and larger cluster sizes.
Example data table
| Scenario | n | m | ICC | Weight CV | Strata factor | Combined deff | Effective n | Adjusted MOE |
|---|---|---|---|---|---|---|---|---|
| National clustered survey with mild weighting | 1200 | 12 | 0.03 | 0.25 | 0.95 | 1.3425 | 893.88 | 3.48% |
Formula used
Cluster effect: Deffcluster = 1 + (m − 1)ρ
Weight effect: Deffweight = 1 + CVw2
Total effect: Defftotal = Deffcluster × Deffweight × Fstrata
Effective sample size: neff = n ÷ Defftotal
Adjusted margin of error: MOEadj = MOESRS × √Defftotal
The cluster term measures within-cluster similarity. The weighting term captures variance inflation caused by unequal analysis weights. The stratification factor lets you model precision gains from well-built strata or losses from imperfect implementation. Multiplying the three components gives a practical combined design effect for planning and reporting.
How to use this calculator
- Enter the achieved total sample size and a simple-random-sample margin of error benchmark.
- Add the average cluster size and an ICC estimate from prior studies, pilots, or literature.
- Enter the weight coefficient of variation directly, or use weight mean and standard deviation.
- Set the stratification factor. Use 1 for neutral assumptions, below 1 for expected gains.
- Press the calculate button to reveal the results block above the form.
- Use the CSV and PDF buttons to export a compact report for documentation or team review.
Frequently asked questions
1) What does design effect mean?
Design effect compares the variance from a complex sample with the variance from a simple random sample of the same size. Values above 1 mean the design reduces precision. Values below 1 mean the design improves precision.
2) Why does clustering usually increase design effect?
People in the same cluster often share similar traits, behaviors, or environments. That similarity reduces independent information, so the sample behaves like a smaller simple random sample and the variance rises.
3) What is ICC in this calculator?
ICC is the intraclass correlation coefficient. It measures how alike observations are within the same cluster. An ICC near zero means little clustering penalty, while larger values can sharply increase design effect.
4) How do unequal weights affect precision?
Unequal weights can inflate variance because some cases contribute far more than others. The Kish approximation uses one plus the squared coefficient of variation of the weights to estimate that penalty.
5) What does the stratification factor do?
It represents the net precision effect of stratification. Values under 1 imply improved efficiency from strong strata. Values above 1 imply losses, which can happen when strata are poorly aligned with analysis goals.
6) Why is effective sample size useful?
Effective sample size translates complex-design precision into a simple-random-sample equivalent. It helps teams explain why a large raw sample may still behave like a smaller sample once clustering and weighting are considered.
7) Can design effect be less than 1?
Yes. Strong stratification can reduce variance enough to offset clustering or weighting penalties. In that case, the combined design effect falls below 1 and the design becomes more efficient than a simple random sample.
8) Should I report component effects separately?
Yes. Reporting cluster, weight, and stratification components makes assumptions transparent and easier to audit. It also shows whether precision losses come from field design, weighting strategy, or both.