qsturng.hlp.htm

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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
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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
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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
       loesljrgatican.net

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