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From Encyclopedia of Mathematics
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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=55457
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article