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Re: st: non parametric tests


From   Roger Newson <roger.newson@kcl.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: non parametric tests
Date   Wed, 10 Aug 2005 19:24:39 +0100

At 18:11 10/08/2005, Ronan M Conroy wrote:
n j cox wrote:

stefania_ottone

 >>> Is the spearman test run in stata corrected for ties?

In -spearman- the correlation is just the Pearson correlation
calculated on the ranks. Thus Stata does nothing special about
ties. I think Stata here shares in a widespread prejudice: if
ties are an issue for you, then either your sample is too small
or the data are too problematic for Spearman to be appropriate.
Getting the P-value exactly right if the main idea is dubious
is putting the emphasis in the wrong place. No doubt other
software can fill the gap.
The old SPSS manual (Nie, Hull et al) maintaned that Kendall's tau-b was superior to Spearman's rho when there were many ties or a small number of individual values in one of the variables. I am not sure of the evidence for this - does anyone know?
I don't know what SPSS meant by "superior" in this context. However, Kendall and Gibbons (1990) give a lot of reasons for preferring Kendall's tau to Spearman's rho, with or without ties. It is easier to interpret, and the central limit theorem works much faster for Kendall's tau than for Spearman's rho. Spearman's rho mainly caught on because it is easier than Kendall's tau to calculate without a computer, and this was an issue when Maurice Kendall was alive. (I seem to recall that he died in the early 1980s.)

Calculating confidence intervals for Kendall's tau-a was even more difficult without computers. In fact, even Henry Daniels and Maurice Kendall didn't manage to do it without making mistakes, when they gave a worked example of the formulas in in their paper (Daniels and Kendall, 1947).

Roger


References

Daniels, H. E. and Kendall, M. G. 1947. The Significance of Rank Correlation Where Parental Correlation Exists. Biometrika 34: 197-208.

Kendall, M. G. and J. D. Gibbons. 1990. Rank Correlation Methods. 5th edition.
New York: Oxford University Press.


--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
Division of Asthma, Allergy and Lung Biology
King's College London

5th Floor, Capital House
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Tel: 020 7848 6648 International +44 20 7848 6648
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or 020 7848 6605 International +44 20 7848 6605
Email: roger.newson@kcl.ac.uk
Website: http://phs.kcl.ac.uk/rogernewson/

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

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