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| In [[statistics]], the '''design effect''' (or '''estimates of unit variance''') is an adjustment used in some kinds of studies, such as [[cluster randomised trial]]s, to allow for the design structure. The adjustment inflates the [[variance]] of parameter estimates, and therefore their [[Standard error (statistics)|standard error]]s, which is necessary to allow for [[correlation]]s among [[Cluster analysis|clusters]] of observations.<ref>{{cite journal|url=http://intqhc.oxfordjournals.org/cgi/content/full/14/6/521 |title=Design effects and intraclass correlation coefficients from a health facility cluster survey in Benin|author=Alexander K. Rowe, Marcel Lama, Faustin Onikpo and Michael S. Deming|journal=International Journal for Quality in Health Care|year=2002|volume= 14|pages=521–523|issue=6}}</ref><ref>{{cite web|url=http://nces.ed.gov/statprog/2002/glossary.asp |title=Glossary - NCES Statistical Standards}}</ref> It is similar to the [[variance inflation factor]] and is used in [[sample size]] calculations.<ref>{{cite journal | last1 = Heo | first1 = Moonseong | last2 = Kim | first2 = Yongman | last3 = Xue | first3 = Xiaonan | last4 = Kim | first4 = Mimi Y. | year = 2010 | title = Sample size requirement to detect an intervention effect at the end of follow-up in a longitudinal cluster randomized trial | url = http://www3.interscience.wiley.com/journal/123212319/abstract | journal = Statistics in Medicine | volume = 29 | issue = 3| pages = 382–390 }}</ref> The term was introduced by [[Leslie Kish]] in 1965.<ref name=Kish>{{cite journal |author=Kish, Leslie |title=Survey Sampling |location=New York |publisher=John Wiley & Sons, Inc. |year=1965|ISBN=0-471-10949-5}}</ref>
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| ==Definition==
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| For a cluster randomised trial with ''m'' observations in each cluster and [[intra-cluster correlation]] of <math>\rho</math>, the design effect. ''D''<sub>eff</sub>, is given by:<ref>Bland, M (2005), [http://www-users.york.ac.uk/~mb55/talks/clusml.htm "Cluster randomised trials in the medical literature"], Notes for talks, York Univ</ref>
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| :<math> D_\text{eff} = 1 + (m - 1) \rho .</math>
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| Formally, the design effect is the ratio of two theoretical variances for an [[estimator]]:<ref name=Kish/><ref>Everitt, B.S. (2002) ''The Cambridge Dictionary of Statistics'', 2nd Edition. CUP. ISBN 0-521-81099-X </ref>
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| :*the actual variance for a given sampling design;
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| :*the variance assuming the same sample size, but using simple random sampling without replacement.
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| ==References==
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| {{reflist}}
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| [[Category:Medical statistics]]
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| [[Category:Design of experiments]] | |
Latest revision as of 21:21, 18 August 2014
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