Studentized range
A statistic from the class of so-called Studentized statistics, obtained as a result of a special normalization of a linear combination of order statistics constructed from a normal sample.
Let be independent normally
-distributed random variables, and let
be the vector of order statistics constructed from the observations
. Moreover, let the statistic
, which is a linear combination of the order statistics
, be independent of some "chi-squared" distribution
of
degrees of freedom. Let
. In this case, one says that
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is a Studentized statistic.
The Studentized range is the Studentized statistic for which is the range of the sample
, i.e. if
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consequently, the Studentized range takes the form
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References
[1] | H. David, "Order statistics" , Wiley (1970) |
[2] | S.S. Wilks, "Mathematical statistics" , Wiley (1962) |
Comments
The case
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is used for tests of normality and outlying observations, cf. [1], Chapt. 8. For a table of the quantiles of the Studentized range see [a2].
References
[a1] | A.M. Mood, F.A. Graybill, "Introduction to the theory of statistics" , McGraw-Hill (1963) pp. 243 |
[a2] | P.H. Müller, P. Neumann, R. Storm, "Tafeln der mathematischen Statistik" , C. Hauser (1977) pp. 166–169 |
Studentized range. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Studentized_range&oldid=11560