Blocking (statistics)

In the statistical theory of the design of experiments, blocking is the arranging the experimental units in groups (blocks) which are similar to one another. For example, instead of a group of patients taking a new drug and a control group of patients taking a placebo, one has a two such groups of male patients and two such groups of female patients. "Drug" and "placebo" are "treatments"; "male" and "female" are "blocks". 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 2n volunteers, give n of them shoes with the new soles and n of them regular shoes. The assignment of new or regular soles should be by randomization. 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. The choice of assigning the new sole to the right or left shoe should be by randomization. Such a design is called a randomized complete block design. This design will be more sensitive than the first, because each person is acting as their own control and thus the control group is more closely matched to the treatment group. The theoretical basis of blocking is the following mathematical result. Given random variables, X and Y

Related Topics:
Statistical - Design of experiments - Experimental unit - Randomization - Control group - Treatment group

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:

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operatorname{var}(X-Y)= operatorname{var}(X) + operatorname{var}(Y) - 2operatorname{cov}(X,Y).

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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.

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