Re: st: RE: Measures of association for a small sample

["Roger B. Newson" <r.newson@imperial.ac.uk>]

I would second the recommendation of -ktau-, but would be less keen on 
-spearman-. The Daniels permutational limit theorem is a version of the 
Central Limit Theorem that works very quickly for Kendall's tau-a but 
not so quickly for Spearman's rho. For Kendall's tau-a with continuous 
data, the null distribution is almost indistinguishable even at N=8. See 
Kendall and Gibbons (1990).

Of course, if you want a confidence interval for Kendall's tau-a instead 
of just a P-value, then you can use the -somersd- package, downloadable 
from SSC. This should produce sensible results for N=18. As in:

somersd X Y, taua transf(z)

which gives an asymmetric confidence interval for Kendall's tau-a, using 
the delta-jackknife method and the Normalizing and variance-stabilizing 
Fisher z-transform.

I hope this helps.

Best wishes

Roger


References

Kendall, M. G., and J. D. Gibbons. 1990. Rank Correlation Methods. 5th 
ed. Oxford, UK: Oxford University Press.

Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

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

On 10/01/2012 23:01, Steve Samuels wrote:
> I believe that Francisco used the word "population" in a loose sense, because he didn't realize that it has a technical meaning in statistics.  I think he means "sample".  To solve his problem I suggest -spearman- or -ktau-.
>
> Steve
>
>
> On Jan 10, 2012, at 10:31 AM, Lachenbruch, Peter wrote:
>
> If you have the entire population, why do you need significance tests?  Isn't the measure sufficient?
>
> ________________________________________
> From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] On Behalf Of Francisco Rowe [frowe@ucn.cl]
> Sent: Tuesday, January 10, 2012 4:35 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Measures of association for a small sample
>
> Hi,
>
> Sorry for taking advantage of statalist for this -I am trying to measure the association between two variables with a reduced number of observations (13) which constitutes my entire population.
>
> I have utilised pairwise correlation coefficients (pwcorr) and regression using an Iteratively Reweighted Least Squares (IRLS) estimation (rreg) (on cross-sectional data). However, given some of the assumptions of these measures, the results can be questioned. For this reason, I would like to implement some additional tests or measures on my data.
>
> Would it be possible to have some guidance on this?
> Are regressions based on IRLS useful in this context?
> Which non-parametric measure can it be useful?
>
> Thanks in advance.
>
> Francisco.
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