Design Effect & Effective Sample Size Calculator
See how much clustering costs you in statistical power. Enter your sample size, the average responses per cluster and the intra-cluster correlation.
Learn how to calculate it yourselfEnter your values
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Design effect
- Effective sample size
- 455
Calculate it yourself
Suppose clusters average 20 people, the within-cluster correlation is 0.05 and the survey has 390 responses.
Follow this worked example, then repeat the steps with your own numbers.
Find the cluster contribution
(average cluster size − 1) × correlation = (20 − 1) × 0.05 = 0.95.Add one to get the design effect
DEFF = 1 + 0.95 = 1.95.This is a variance multiplier relative to simple random sampling.
Calculate the effective sample size
Effective n = actual n ÷ DEFF = 390 ÷ 1.95 = 200.For the same assumptions, standard errors are multiplied by √1.95, not by 1.95.
This approximation describes clustering. Unequal weights, stratification and widely varying cluster sizes can require a fuller survey-design calculation.
Check your answer in the calculatorUse your PaperSurvey.io results
Combine your collected count with your sampling design’s cluster information to estimate effective sample size here.
Why clustered samples count for less
When you collect responses in clusters, such as several classrooms, clinics or stores, people within a cluster tend to be similar to each other. That similarity means a clustered sample carries less information than a simple random sample of the same size, so its results are less precise than the raw count of responses suggests.
The formulas
The design effect is 1 + (m − 1) × ICC, where m is the average cluster size and ICC is the intra-cluster correlation. The effective sample size is your actual sample size divided by the design effect. It is the size of a simple random sample that would give the same precision, and it is the number to use when planning margins of error.
Frequently asked questions
What ICC should I use?
If you have no prior data, values between 0.01 and 0.05 are common for large surveys, though tightly clustered outcomes can be higher. Use an estimate from a similar past study when you can.
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