Statistics Definitions > Design Effect

## What is a Design Effect?

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).

Where:

- δ = interclass correlation for the statistic.
- n = average size of the cluster.

**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.

**Need help with a homework or test question? **With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free!

*Statistical concepts explained visually* - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.

**Comments? Need to post a correction?** Please post a comment on our *Facebook page*.