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From |
Francisco Rowe <frowe@ucn.cl> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Thu, 12 Jan 2012 08:47:00 +1000 |

Thanks Roger, Peter and Nick (you are right the dataset corresponds to the 13 regions of Chile -15 after 2007) for your valuable comments, I will try to implement your suggestions. FR. On 12/01/2012, at 4:50 AM, Nick Cox wrote: > 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/ * * 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/

**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>

**RE: st: RE: Measures of association for a small sample***From:*Nick Cox <n.j.cox@durham.ac.uk>

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