Restricted randomization: Difference between revisions

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In [[statistics]], '''restricted randomization''' occurs in the [[design of experiments]]s 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=0-19-920613-9}}</ref><ref>{{cite journal|last1=Grundy|first1=P.M.|last2=Healy|first2=M.J.R.|title=Restricted randomization and quasi-Latin squares|journal=[[Journal of the Royal Statistical Society]], Series B|volume=12|pages=286-291}}</ref> For example, in a [[clinical trial]] of a new proposed treatment compared to a control, an experimenter would want to avoid outcomes of the randomization in which new treatment was allocated only to the the heaviest patients.

In [[statistics]], '''restricted randomization''' occurs in [[experimental design]]s with more than one source of [[statistical dispersion|variability]]. The concept was introduced by [[Frank Yates]] (1948) and [[William J. Youden]] (1972) "as a way of avoiding bad spatial patterns of treatments in designed experiments."<ref name="ref1">Bailey, R. A. [http://www.jstor.org/discover/10.2307/2288775?uid=3739808&uid=2&uid=4&uid=3739256&sid=21100687318461 Restricted Randomization: A Practical Example], ''Journal of the American Statistical Association'', Vol. 82, No. 399 (Sep., 1987), pp. 712–719, at 712</ref>

In [[statistics]], '''restricted randomization''' occurs in [[experimental design]]s with more than one source of [[statistical dispersion|variability]]. The concept was introduced by [[Frank Yates]] (1948){{full}} and [[William J. Youden]] (1972){{full}} "as a way of avoiding bad spatial patterns of treatments in designed experiments."<ref name="ref1">Bailey, R. A. (1987) [http://www.jstor.org/discover/10.2307/2288775?uid=3739808&uid=2&uid=4&uid=3739256&sid=21100687318461 "Restricted Randomization: A Practical Example"], ''Journal of the American Statistical Association'', Vol. 82, No. 399 (Sep., 1987), pp. 712–719, at 712</ref>

In order to [[variance reduction|reduce variation]] in processes, these multiple sources must be understood, and that often leads to the concept of nested or hierarchical data structures. For example, in the [[semiconductor]] industry, a [[batch production|batch process]] may operate on several [[wafer (electronics)|wafers]] at a time (wafers are said to be '''nested''' within batch). Understanding the input variables that control variation among those wafers, as well as understanding the variation across each wafer in a run, is an important part of the strategy for minimizing the total variation in the system.

==Example of nested data==