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help for ^qsturng^                                (STB-46: dm64)
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Approximate a studentized range quantile
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   ^qsturng^ r nu p


Description
-----------

^qsturng^ computes an approximation to the ^p^-th quantile of the studentized range
distribution for ^r^ means and ^nu^ degrees of freedom, q_p(r, nu).  The studentiz-
ed range is the difference between the maximum and the minimum of ^r^ independent
and identically distributed Gaussian variables, divided by an independent esti-
mate of their standard deviation having ^nu^ degrees of freedom.  The probability
that this statistic exceeds q_p(r, nu) is 1-p.

Studentized range upper quantile points are required by the Tukey wsd multiple
comparison method, among several other techniques.  ^qsturng^ calculates approxi-
mate quantiles for such uses; the approximation error is rarely larger than one
unit in the fourth significant digit, accuracy comparable to the best available
tables of the studentized range distribution.


Parameters
----------

^r^  the number of independent normal variates --- means, in the Tukey wsd method
   (2 <= r <= 100).  Extrapolations to r = 200 give errors no larger than about
   one unit in the third significant digit.

^nu^  the degrees of freedom for the scale estimator used to studentize the range
   (nu >= 1).  Fractional degrees of freedom are acceptable.

^p^  the area in the studentized range distribution to the left of the quantile
   computed (0.5 <= p <= 0.999).  Extrapolation to p = 0.9999 is about as accu-
   rate as extrapolation to r = 200.  Extrapolation to p < 0.5 is permitted but
   not encouraged.


Notes
-----

^qsturng^ relies on 8 accessory subroutines to create needed constants.
^qsturng^ uses them to create matrices with names of the form ^StuRng10^, ^StuRng11^,
etc.  In most cases, only one such matrix will be created.

qsturng saves its approximation to q_p(r, nu) in global macro ^S_1^.


Examples
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 . ^qsturng 5 20 0.95^        [display q_0.95(5, 20)]

 . ^qsturng 5 . 0.95^         [display q_0.95(5, Infinity)]

 . ^qsturng 7 43.7 0.99^      [display q_0.99(7, 43.7)]

 . ^qui qsturng 7 43.7 0.99^
 . ^di $S_1^                  [display q_0.99(7, 43.7) to greater accuracy]


Author
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       John R. Gleason
       Syracuse University
       loesljrg@@ican.net


Also see
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    STB: dm64 (STB-46) 
 Manual: ^[U] 20 Functions and expressions^
On-line: help for @functions@