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

[Nick Cox <n.j.cox@durham.ac.uk>]

I guess there is some support for a kind of arm-waving argument that treating the data _as if_ they were a random sample at least provides a context for assessing the magnitude of association observed in that dataset. Plenty of researchers have it both ways by citing a P-value or confidence interval and flagging some reservations about whether that is valid. 

However, a sample of 13 regions is difficult to imagine without some spatial dependence, and none of the procedures cited in this thread I think make any allowance for that. [I guess that concretely we are talking about some relation to the 15 regions of Chile, perhaps with some amalgamations for research purposes.] 

Also, even monotonic correlation is still a subset of association or dependence. 

I am not a great fan of general tests for dependence but FWIW no-one else seems aware of -bkrosenblatt- (SSC). 

Distance correlation in the sense of 

http://en.wikipedia.org/wiki/Distance_correlation

sounds a better procedure than the Blum-Kiefer-Rosenblatt test, but I am not aware of a Stata implementation. 

Nick 
n.j.cox@durham.ac.uk 

Roger B. Newson

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.

References

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

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-.

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?

Francisco Rowe [frowe@ucn.cl]

> 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?
>

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