Restricted randomization: Difference between revisions

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In [[statistics]], '''restricted randomization''' occurs in the [[design of experiments]] and in particular in the context of [[randomized experiment]]s and [[randomized controlled trial]]s. Restricted randomization allows intuitively poor allocations of treatments to experimental units to be avoided, while retaining the theoretical benefits of randomization.<ref>{{cite book|last1=Dodge| first1= Y.|title=The Oxford Dictionary of Statistical Terms|publisher=OUP|year=2006|isbn=978-0-19-920613-91|url-access=registration|url=https://archive.org/details/oxforddictionary0000unse}}</ref><ref>{{cite journal|last1=Grundy|first1=P.M.|last2=Healy|first2=M.J.R.|authorlink2author-link2=Michael Healy (statistician)|title=Restricted randomization and quasi-Latin squares|journal=[[Journal of the Royal Statistical Society]], Series B|date=1950 |volume=12|issue=2 |pages=286–291 |doi=10.1111/j.2517-6161.1950.tb00062.x }}</ref> For example, in a [[clinical trial]] of a new proposed treatment of obesity compared to a control, an experimenter would want to avoid outcomes of the randomization in which the new treatment was allocated only to the heaviest patients.

The concept was introduced by [[Frank Yates]] (1948){{full citation needed|date=November 2012}} and [[William J. Youden]] (1972){{full citation needed|date=November 2012}} "as a way of avoiding bad spatial patterns of treatments in designed experiments."<ref name="ref1">Bailey,{{Cite R.journal A.|jstor (1987)= [http://www.jstor.org/discover/10.2307/2288775?uid|title =3739808&uid=2&uid=4&uid=3739256&sid=21100687318461 "Restricted Randomization: A Practical Example"],|last1 = Bailey|first1 = R. A.|journal = ''Journal of the American Statistical Association'',|year Vol.= 1987|volume = 82,|issue No.= 399|pages (Sep., 1987), pp.= 712–719,|doi at= 71210.1080/01621459.1987.10478487}}</ref>

==Example of nested data==

Consider a batch process that uses 7 monitor [[wafer|wafers]] in each run. The plan further calls for measuring a [[response variable]] on each wafer at each of 9 sites. The organization of the [[sampling plan]] has a hierarchical or nested structure: the batch run is the topmost level, the second level is an individual wafer, and the third level is the site on the wafer.

The total amount of data generated per batch run will be 7&nbsp;·&nbsp;9&nbsp;=&nbsp;63 observations. One approach to analyzing these data would be to compute the [[mean]] of all these points as well as their [[standard deviation]] and use those results as responses for each run.

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==See also==

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* [[Hierarchical linear modeling]]

* [[Mixed-design analysis of variance]]

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==References==

{{reflist}}

* {{cite web | url=http://www.itl.nist.gov/div898/handbook/pri/section5/pri55.htm | title=How can I account for nested variation (restricted randomization)? | publisher=(U.S.) National Institute of Standards and Technology: Information Technology Laboratory | accessdateaccess-date=March 26, 2012}}

==Further reading==

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==External links==

* [httphttps://www.southampton.ac.uk/~cpd/anovas/datasets/index.htm Examples of all ANOVA and ANCOVA models with up to three treatment factors, including randomized block, split plot, repeated measures, and Latin squares, and their analysis in R]

{{Statistics}}