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From |
Nick Cox <n.j.cox@durham.ac.uk> |

To |
"'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu> |

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

Date |
Wed, 11 Jan 2012 18:50:23 +0000 |

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? > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: RE: Measures of association for a small sample***From:*Francisco Rowe <frowe@ucn.cl>

**References**:**st: Measures of association for a small sample***From:*Francisco Rowe <frowe@ucn.cl>

**st: RE: Measures of association for a small sample***From:*"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>

**Re: st: RE: Measures of association for a small sample***From:*Steve Samuels <sjsamuels@gmail.com>

**Re: st: RE: Measures of association for a small sample***From:*"Roger B. Newson" <r.newson@imperial.ac.uk>

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