Difference between revisions of "Contrast"
From Encyclopedia of Mathematics
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Contrasts are invariant under addition of all components of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025960/c0259608.png" /> by the same constant, and therefore do not depend on the arbitrary "general level" of the measurements. This can be a great advantage in certain settings. | Contrasts are invariant under addition of all components of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025960/c0259608.png" /> by the same constant, and therefore do not depend on the arbitrary "general level" of the measurements. This can be a great advantage in certain settings. | ||
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Revision as of 14:10, 8 April 2023
comparison
The scalar product 
of a vector 
whose coordinates are unknown parameters, by a given vector 
such that 
. For example, the difference 
of the unknown mathematical expectations 
and 
of two one-dimensional normal distributions is a contrast. In analysis of variance, the problem of multiple comparison if often considered; this problem is concerned with the testing of hypotheses concerning the numerical values of several contrasts.
References
| [1] | H. Scheffé, "Analysis of variance" , Wiley (1959) |
Comments
Contrasts are invariant under addition of all components of 
by the same constant, and therefore do not depend on the arbitrary "general level" of the measurements. This can be a great advantage in certain settings.
How to Cite This Entry:
Contrast. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Contrast&oldid=12403
Contrast. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Contrast&oldid=12403
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article