Blocking (statistics)

Blocking (statistics)

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 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 a completely 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 where random assignment of the two treatments to the left or right shoe of each volunteer is conducted. 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"

: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

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Blocking — may refer to:In telecommunications: *Block size (data storage and transmission), the formatting of data into blocks for purposes of transmission, storage, checking, or other functions *Block storage, a sequence of bytes or bits, having a nominal… …   Wikipedia

  • statistics — /steuh tis tiks/, n. 1. (used with a sing. v.) the science that deals with the collection, classification, analysis, and interpretation of numerical facts or data, and that, by use of mathematical theories of probability, imposes order and… …   Universalium

  • List of statistics topics — Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… …   Wikipedia

  • Comparison of statistics journals — This is a comparison of peer reviewed scientific journals published in the field of statistics. Contents 1 General information 2 Impact, indexing, abstracting and reviewing 3 Notes 4 …   Wikipedia

  • Official statistics — on Germany in 2010, published in UNECE Countries in Figures 2011. Official statistics are statistics published by government agencies or other public bodies such as international organizations. They provide quantitative or qualitative information …   Wikipedia

  • Outline of statistics — The following outline is provided as an overview and guide to the variety of topics included within the subject of statistics: Statistics pertains to the collection, analysis, interpretation, and presentation of data. It is applicable to a wide… …   Wikipedia

  • Descriptive statistics — quantitatively describe the main features of a collection of data.[1] Descriptive statistics are distinguished from inferential statistics (or inductive statistics), in that descriptive statistics aim to summarize a data set, rather than use the… …   Wikipedia

  • Mathematical statistics — is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis. The term mathematical statistics is closely related to the term statistical theory… …   Wikipedia

  • Multivariate statistics — is a form of statistics encompassing the simultaneous observation and analysis of more than one statistical variable. The application of multivariate statistics is multivariate analysis. Methods of bivariate statistics, for example simple linear… …   Wikipedia

  • Errors and residuals in statistics — For other senses of the word residual , see Residual. In statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of the deviation of a sample from its theoretical value . The error of a… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”