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

 From Francisco Rowe To statalist@hsphsun2.harvard.edu Subject Re: st: RE: Measures of association for a small sample Date Fri, 13 Jan 2012 13:37:22 +1000

```Adding another layer to this discussion -I have consulted the Stata manual, Efron and Tibshirani (1993) and Cameron and Trivedi (2009)-, thus far, there seems to be no consensus about which p-values or confidence intervals should be presented in a publication either using a particular method (the normal-based method, the percentile method, the bias-correct method, the bias-corrected accelerated method, or the approximate bootstrap confidence method) or a specific group of them, while considering not to overwhelm the reader or audience with little background on bootstrapping.

Is it wrong?

- An additional question is: how can I compute confidence intervals based on the percentile method after bootstrapping? I tried:

bootstrap r(rho), reps(1000) seed(1) saving("bs_MNI.dta", double replace): corr varE varNI if Sex==0
use “bs_MNI.dta”, clear
centile (_bs_1), centile (2.5 97.5)
where: _bs_1 corresponds to the bootstrap estimates.

but I do not get the same results after bootstrapping.

Regards,
FR.

On 11/01/2012, at 3:03 PM, Robert A Yaffee wrote:

> Francisco,
>   You are skating on thin statistical ice.  But with such a small sample size
> you have what Damodar Gujarati calls the problem of micro-numerosity,
> which his what others call finite samples, which are
> not in general conformity with the laws of large numbers.  This is
> territory where asymptotics are not going to be of much help
> in attaining a population estimate.  You might want to do a power
> analysis to get an idea of your probability of failing to detect
> a significance of a medium effect size.
>
>   You could consider bootstrapping or permutation tests if you were
> sure that your data were representative.
>         Regards,
>             Robert
>
> On Tue, Jan 10, 2012 at 10:31 AM, Lachenbruch, Peter
> <Peter.Lachenbruch@oregonstate.edu> 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?
>>
>>
>> Francisco.
>> *
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>
>
>
> --
> Robert A. Yaffee, Ph.D.
> Research Professor
> Silver School of Social Work
> New York University
>
> Biosketch: http://homepages.nyu.edu/~ray1/Biosketch2009.pdf
>
> CV:  http://homepages.nyu.edu/~ray1/vita.pdf
>
> *
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*
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```