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Multiple comparison

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The problem of testing hypotheses with respect to the values of scalar products of a vector , the coordinates of which are unknown parameters, with a number of given vectors . In statistical research the multiple comparison problem often arises in dispersion analysis where, as a rule, the vectors are chosen so that , and the scalar product itself, in this case, is called a contrast. On the assumption that are unknown mathematical expectations of one-dimensional normal laws, J.W. Tukey and H. Scheffé proposed the -method and the -method, respectively, for the simultaneous estimation of contrasts, which are the fundamental methods in the problem of constructing confidence intervals for contrasts.

References

[1] H. Scheffé, "The analysis of variance" , Wiley (1959)
[2] M.G. Kendall, A. Stuart, "The advanced theory of statistics" , 3. Design and analysis, and time series , Griffin (1983)


Comments

References

[a1] R. Miller, "Simultaneous statistical inference" , McGraw-Hill (1966)
How to Cite This Entry:
Multiple comparison. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Multiple_comparison&oldid=11413
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article