In statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, the design effect is an adjustment used in some kinds of studies, such as cluster randomised trials, to allow for the design structure. The adjustment inflates the variance

Variance

In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...

 of parameter estimates, and therefore their standard error

Standard error (statistics)

The standard error is the standard deviation of the sampling distribution of a statistic. The term may also be used to refer to an estimate of that standard deviation, derived from a particular sample used to compute the estimate....

s, which is necessary to allow for correlation

Correlation

In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....

s among cluster

Cluster

-In science:* Cluster , a small group of atoms or molecules* Cluster chemistry, an array of bound atoms intermediate in character between a molecule and a solid...

s of observations. It is similar to the variance inflation factor

Variance inflation factor

In statistics, the variance inflation factor quantifies the severity of multicollinearity in an ordinary least squares regression analysis...

 and is used in sample size

Sample size

Sample size determination is the act of choosing the number of observations to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample...

 calculations. The term was introduced by Leslie Kish

Leslie Kish

Leslie Kish was an American statistician and survey methodologist of Hungarian descent. He fought in the International Brigade in the Spanish Civil War....

 in 1965.

Definition

For a cluster randomised trial with m observations in each cluster and intra-cluster correlation of , the design effect. D_eff, is given by:


Formally, the design effect is the ratio of two theoretical variances for an estimator

Estimator

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule and its result are distinguished....

:

• the actual variance for a given sampling design;
• the variance assuming the same sample size, but using simple random sampling without replacement.