Re: st: non parametric tests

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

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

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

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