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st: RE: RE: Signtest (statistics question)


From   Roger Newson <[email protected]>
To   [email protected]
Subject   st: RE: RE: Signtest (statistics question)
Date   Mon, 12 May 2003 16:08:39 +0100

At 15:38 12/05/03 +0100, Nick Cox wrote:

Cue Roger Newson, for an exordium on the
merits of Somers' d...

("Shall I compare thee to a Somers' d?" W. Shakespeare,
Sonnets, modern reading)
As it happens, the sign test tests for a zero value for the difference between 2 conditional probabilities

Pr(x1>x2 | x1!=x2) - Pr(x1<x2 | x1!=x2)

which is, in a way, a special case of Somers' D, which is also a difference between 2 conditional probabilities. The Somers' D calculated by my -somersd- package (downloadable from SSC) is like the two-sample t-test, whereas the difference tested by the sign test is like the paired t-test.

The difference between the 2 corresponding unconditional probabilities

Pr(x1>x2) - Pr(x1<x2)

is similarly a paired version of Kendall's tau-a.

More on Somers' D, Kendall's tau-a and median differences can be found in my Stata Journal insert on the subject (Newson, 2002).

As it happens, I did some work on paired (or more general within-group) versions of Kendall's tau-a in my DPhil thesis (Newson, 1987). I have always wanted to generalise the -somersd- package to the within-group case, and to the case of survival analysis, but have always thought that I would need DLLs to do this properly. Not surprisingly, I am looking forward to hearing what Bobby Gutierrez and Nguyen Chinh have to say on DLLs at the 9th UK Stata User Meeting.

Best wishes

Roger

References

Newson RB. An analysis of cinematographic cell division data using U-statistics. DPhil dissertation. Brighton, UK: Sussex University; 1987.

Newson R. Parameters behind "nonparametric" statistics: Kendall's tau, Somers' D and median differences. The Stata Journal 2002; 2(1): 45-64.


--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
5th Floor, Capital House
42 Weston Street
London SE1 3QD
United Kingdom

Tel: 020 7848 6648 International +44 20 7848 6648
Fax: 020 7848 6620 International +44 20 7848 6620
or 020 7848 6605 International +44 20 7848 6605
Email: [email protected]

Opinions expressed are those of the author, not the institution.

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