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st: RE: Stata Program to Conduct Tests of Stochastic Dominance?


From   Roger Newson <[email protected]>
To   [email protected]
Subject   st: RE: Stata Program to Conduct Tests of Stochastic Dominance?
Date   Wed, 15 Oct 2003 12:31:23 +0100

At 10:14 15/10/03 +0100, Nick Cox wrote:
Cruces,GA

> I was wondering if there is any program - standard or
> user-written - to
> perform tests of dominance between distributions. I only
> know ksmirnov
> for tests of equality of distribution, and there are some
> graphic tools
> to perform similar analisys (glcurve, cdf, etc.).

Whenever I see the word "test", I reach for an
estimation procedure.

If you are comparing distributions of two groups,
-ranksum- has a -porder- option which gives an
estimate of the probability that the variable
for the first group is larger than the variable
for the second group. This often is more scientific
use than a P-value.
The confidence interval corresponding to -ranksum- can be for one of 2 things, namely the Hodges-Lehmann median difference or Somers' D. (Somers' D is defined as the difference between 2 probabilities, namely the probability that a randomly-chosen member of Group A has a higher value than a randomly-chosen member of Group B and the probability that a randomly-chosen member of Group B has a higher value than a randomly-chosen member of Group A.)

Confidence intervals for both these parameters can be calculated in Stata using the -somersd- package, which can be downloaded from SSC, and contains 2 programs, -somersd- (for calculating CIs for Somers' D and Kendall's tau-a) and -cendif- (which calculates CIs for median differences). The methods behind the package are discussed in Newson (2002), and a pre-publication draft of this paper can be downloaded from my website at

http://www.kcl-phs.org.uk/rogernewson/

either using a browser or using the Stata -net- command.

I hope this helps.

Roger

References

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]
Website: http://www.kcl-phs.org.uk/rogernewson

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

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