Design Effect: Definition, Examples

Statistics Definitions > Design Effect

What is a Design Effect?

design effect
A design effect is used to calculate effective sample sizes.
A design effect(DEFF) is an adjustment made to find a survey sample size, due to a sampling method (e.g. cluster sampling, respondent driven sampling, or stratified sampling) resulting in larger sample sizes (or wider confidence intervals) than you would expect with simple random sampling(SRS). The DEFF tells you the magnitude of these increases.

The design effect is the ratio of the actual variance to the variance expected with SRS. It can more simply be stated as the actual sample size divided by the effective sample size (the effective sample size is what you would expect if you were using SRS). For example, let’s say you were using cluster sampling. A DEFF of 2 means the variance is twice as large as you would expect with SRS. It also means that if you used cluster sampling, you’d have to use twice the sample size.

Formula for DEFF

The formula to find the design effect is:

DEFF = 1 + δ(n – 1).


Caution: Design effects found in one survey should not automatically be used in other surveys. Before you use a DEFF from another survey, make sure that all the components (e.g. the interclass correlation and sample size) are the same.

Other Definitions

You might see the DEFF defined in terms of standard errors. That’s because the DEFF makes adjustments to the variances — and therefore the standard errors. The term “design effect” has also taken on another meaning in statistics literature — as the ratio of the standard errors, called deft. As √deft is equal to deff, it’s easy to convert from one to another. Just be aware of which equation you’re using.

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