Thanks to Nick for the reference.
I would agree that one c-index with confidence limits (or the difference
between 2 such c-indices) is more interesting than the corresponding
P-value. However, P-values may come into their own when we calculate a
lot of them, as in a genome scan, and want to use them in a
multiple-test procedure. If the sample size is not too large, then the
test-based P-value, calculated by -ranksum- using a test-based standard
error, may be a more reliable P-value than that currently produced by
-somersd-, using an estimation-based standard error. This
estimation-based standard error may collapse to zero if Somers' D (and
therefore the c-index) is one, implying a zero P-value which possibly
shouldn't be trusted far in a small sample. Therefore, -ranksum- and
-ktau- are complementary to -somersd-.
Roger
Roger Newson
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: [email protected]
www.imperial.ac.uk/nhli/r.newson/
Opinions expressed are those of the author, not of the institution.
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Nick Cox
Sent: 12 June 2007 18:05
To: [email protected]
Subject: st: RE: RE: ranksum: p-value?
No disrespect to Frank Harrell, but the fact that
the Wilcoxon-Mann-Whitney test is intelligible
in terms of this probability long predates Harrell's
work. As I recall it surfaces in the literature about
1950. One reference is Z.W. Birnbaum. 1956.
On a use of the Mann-Whitney statistic,
Proc. 3rd. Berkeley Symp. Mathematical Statistics &
Probability, vol 1, which gives earlier references.
Anyway, it is far more interesting than the P-value!
Nick
[email protected]
Newson, Roger B
> Your true P-value is
>
> Prob > z = 0.0216
>
> The other probability (0.604) is not a P-value, but is the probability
> that a randomly-chosen member of Group A has a higher outcome
> value than
> a randomly-chosen member of Group B. This probability is known as
> Harrell's c-index. If you want a confidence interval for Harrell's
> c-index (or for Somers' D = 2c-1), then you can use the -somersd-
> package, downloadable from SSC using the -ssc- command in Stata. The
> -somersd- package can also estimate median differences, ratios and
> slopes.
Vanessa Mahlberg
> I?ve done a Wilcoxon test for testing the difference between
> two groups.
> Now I have a doubt about the interpretation of the result of
> this test.
> I don?t know which one is my real p-value. The one Prob > z = 0.0216
> or 0.604??? The obtained result is:
>
> .ranksum a_firmenbewertung, by (zugeh) porder
>
> Two-sample Wilcoxon rank-sum (Mann-Whitney) test
>
> zugeh obs rank sum expected
>
> Ehemalige Pr 84 7327.5 6678
> Direkteinste 74 5233.5 5883
>
> combined 158 12561 12561
>
> unadjusted variance 82362.00
> adjustment for ties -2423.03
> ----------
> adjusted variance 79938.97
>
> Ho: a_firm~g(zugeh==Ehemalige Praktikanten) =
> a_firm~g(zugeh==Direkteinsteiger)
> z = 2.297
> Prob > z = 0.0216
>
> P{a_firm~g(zugeh==Ehemalige Praktikanten) >
> a_firm~g(zugeh==Direkteinsteiger)} = 0.604
>
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
