st: RE: RE: Signtest (statistics question)

[Roger Newson <roger.newson@kcl.ac.uk>]

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: roger.newson@kcl.ac.uk

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

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