Blocking (statistics)
Encyclopedia
In the statistical theory of the design of experiments
, blocking is the arranging of experimental units 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 a double 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 intended to make the soles of shoes last longer, and we plan to conduct a field trial. Given a group of n volunteers, one possible design would be to give n/2 of them shoes with the new soles and n/2 of them shoes with the ordinary soles, randomizing
the assignment of the two kinds of soles. This type of experiment is a completely randomized design
. We ask both groups to use their shoes for a period of time, and then measure the degree of wear of the soles. This is a workable experimental design, but purely from the point of view of statistical accuracy (ignoring any other factors), a better design would be to give each person one regular sole and one new sole, randomly assigning the two types to the left and right shoe of each volunteer. 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
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.
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
, blocking is the arranging of experimental units 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
Drug
A drug, broadly speaking, is any substance that, when absorbed into the body of a living organism, alters normal bodily function. There is no single, precise definition, as there are different meanings in drug control law, government regulations, medicine, and colloquial usage.In pharmacology, a...
, and placebo
Placebo
A placebo is a simulated or otherwise medically ineffectual treatment for a disease or other medical condition intended to deceive the recipient...
, administered to male and female patients in a double 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 intended to make the soles of shoes last longer, and we plan to conduct a field trial. Given a group of n volunteers, one possible design would be to give n/2 of them shoes with the new soles and n/2 of them shoes with the ordinary soles, randomizing
Randomization
Randomization is the process of making something random; this means:* Generating a random permutation of a sequence .* Selecting a random sample of a population ....
the assignment of the two kinds of soles. This type of experiment is a completely randomized design
Completely randomized design
In the design of experiments, completely randomized designs are for studying the effects of one primary factor without the need to take other nuisance variables into account. This article describes completely randomized designs that have one primary factor. The experiment compares the values of a...
. We ask both groups to use their shoes for a period of time, and then measure the degree of wear of the soles. This is a workable experimental design, but purely from the point of view of statistical accuracy (ignoring any other factors), a better design would be to give each person one regular sole and one new sole, randomly assigning the two types to the left and right shoe of each volunteer. 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
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.
See also
- Block design
- Paired difference testPaired difference testIn statistics, a paired difference test is a type of location test that is used when comparing two sets of measurements to assess whether their population means differ...
- Randomized block designRandomized block designIn the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups that are similar to one another. Typically, a blocking factor is a source of variability that is not of primary interest to the experimenter...