- Blocking (statistics)
In the

statistical theory of thedesign of experiments ,**blocking**is the arranging ofexperimental unit s in groups (blocks) that are similar to one another. For example, an experiment is designed to test a new drug on patients. There are two levels of the treatment, "drug", and "placebo", administered to "male" and "female" patients in adouble blind trial. The sex of the patient is a "blocking" factor accounting for treatment variability between "males" and "females". This reduces sources of variability and thus leads to greater precision.Suppose we have invented a process which we believe makes the soles of shoes last longer, and we wish to conduct a field trial. One possible design would be to have a group of "n" volunteers, give 0.5"n" of them shoes with the new soles and 0.5"n" of them regular shoes, randomizing (see

randomization ) the assignment of the two types of shoes. This type of experiment is acompletely randomized design .We can then let both groups use their shoes for a suitable period of time and then compare them. A better design would be to give each person one regular sole and one new sole whererandom assignment of the two treatments to the left or right shoe of each volunteer is conducted. Such a design is called arandomized complete block design . This design will be more sensitive than the first, because each person is acting as their own control and thus thecontrol group is more closely matched to thetreatment group . The theoretical basis of blocking is the following mathematical result. Given random variables, "X" and "Y":$operatorname\{Var\}(X-Y)=\; operatorname\{Var\}(X)\; +\; operatorname\{Var\}(Y)\; -\; 2operatorname\{Cov\}(X,Y).$

The difference between the treatment and the control can thus be given minimum variance (i.e. maximum precision) by maximising the covariance (or the correlation) between "X" and "Y".

**ee also***

Block design

*Randomized block design

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