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Re: st: signrank only gives asymptotic p-value?

From   Joseph Coveney <[email protected]>
To   Statalist <[email protected]>
Subject   Re: st: signrank only gives asymptotic p-value?
Date   Fri, 29 Jul 2005 15:52:05 +0900

Jacob Wegelin wrote:

The command

signrank junk

where junk is a variable with the following seven values:

-0.5 1 2 3 4 4.3 4.4

yields a p-value of 0.0280.  (This is Stata/SE 9.0 for Windows.)  This
appears to be the *asymptotic* p-value, i.e., based on computing an
approximate z statistic of 2.197.

This is not the p-value one gets by comparing the signed rank statistic
(which is 1, i.e., the number one) with the distribution of the signed rank
statistic.  That p-value is 0.03125, when computed by R software

My reference for the wilcoxon is van Belle et al., Biostatistics: A
Methodology for the Health Sciences. 2 ed. Hoboken, New Jersey: John Wiley
& Sons, Inc.; 2004, pages 258ff.

The Stata manual (Release 8, 2003, Reference S-Z, page 64-66) supports
my belief that only the asymptotic p-value is returned by Stata, because
the passage on signrank ends with the formula for the z statistic.

Is there a way to get the actual wilcoxon signed-rank p-value, i.e., not
the asymptotic p-value, out of Stata?


You can get there using -permute-.  It's illustrated below with syntax for
Release 9.  You can increase the number of replications to increase
precision as desired.  (The run illustrated below gives 9,391 / 300,000, or
P = 0.0313.)

I think that there is C source code floating around on the Web for the
Wilcoxon signed ranks permutation distribution that you can fashion into a
plug-in that would be quicker, but not so quick as reaching over to the

Joseph Coveney

set more off
input float junk
generate float reference = 0
rename junk junk0
generate float junk1 = -junk0
generate byte row = _n
reshape long junk, i(row) j(flip)
program define longranksum, rclass
    signrank junk = reference if flip
    return scalar z = r(z)
set seed `=date("2005-07-29", "ymd")'
permute flip Z = r(z), reps(300000) strata(row) ///
  nodots nowarn: longranksum

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