Re: [R] permutation test assumption?

From: Ramon Diaz-Uriarte <rdiaz02_at_gmail.com>
Date: Thu, 10 Apr 2008 18:23:12 +0200

Just an additional note: what I find interesting (that is an euphemism) is that a paper such as that got published on 2006 when a whole bunch of detailed papers on the same topic had been published in the past. For instance, the first I pick from the pile is by J. Romano, "On the behavior of randomization tests without a group invariance assumption", JASA, 1990, 85 (411): 686-692. There are other related papers on that same issue of JASA. The relevance of same-variance assumption also shows up in permutation test textbooks (including, I think, Manly's, Good's, Noreen's, etc).

Best,

R.

On Wed, Apr 9, 2008 at 9:11 PM, Greg Snow <Greg.Snow_at_imail.org> wrote:
> A few comments,
>
> My first impression on reading that abstract was that it was complete nonsense. After thinking a bit about it and skimming the full article I decided that it was nonsense, but nonsense that is important to research and discuss (and therefore the paper is useful).
>
> Why is it nonsense? The permutation test is a test of the null hypothesis that the 2 (or k) groups are from the same distribution (or identically distributed, or exchangable). The abstract says that they looked at the type I error rate when the 2 groups had different variances or other differences. The type I error is defined when the null hypothesis is true, so computing a type I error rate when the null is by definition false does not make sense.
>
> However, statisticians often do analyses where all the assumptions are not necessarily true (is any population really distributed as a normal), but the tests are close enough. So with modern tools it is not suprising to see people doing permutation tests without understanding what they are really testing and the results may be close enough (or they might not be). The contribution of this paper is to test and see if the results are close enough or not when you use a permutation test to test the null that the means are equal when there are other differences in the groups. Their answer is that no, the results are not close enough and they suggest that if you want to test for equality of means, but not identical distributions, then don't use a permutation test.
>
> To expand on Thierry's original answer:
>
> If you are testing the correct hypotheses and doing a permutation test correctly, then
> "You can do permutation tests on an unbalanced design" and it will still be a correct test. Unbalance could affect the power, which you would want to take into account when designing a study, but does not affect the correctness of the test (when used properly).
>
> Hope this helps,
>
> --
> Gregory (Greg) L. Snow Ph.D.
> Statistical Data Center
> Intermountain Healthcare
> greg.snow_at_imail.org
> (801) 408-8111
>
>
>
>
> > -----Original Message-----
> > From: r-help-bounces_at_r-project.org
> > [mailto:r-help-bounces_at_r-project.org] On Behalf Of Joćo Fadista
> > Sent: Tuesday, April 08, 2008 4:10 PM
>
>
> > To: ONKELINX, Thierry; r-help_at_r-project.org
> > Subject: Re: [R] permutation test assumption?
> >
> > Dear Thierry,
> >
> > Thanks for the reply. But as you may read in the paper
> > http://bioinformatics.oxfordjournals.org/cgi/content/abstract/
> > 22/18/2244 when the sample sizes are not the same there may
> > be an increase in the Type I error rate.
> >
> > Comments will be appreciated.
> >
> > Best regards,
> > Joćo Fadista
> >
> >
> > ________________________________
> >
> > De: ONKELINX, Thierry [mailto:Thierry.ONKELINX_at_inbo.be]
> > Enviada: ter 08-04-2008 15:27
> > Para: Joćo Fadista; r-help_at_r-project.org
> > Assunto: RE: [R] permutation test assumption?
> >
> >
> >
> > Dear Joćo,
> >
> > You can do permutation tests on an unbalanced design.
> >
> > HTH,
> >
> > Thierry
> >
> >
> > --------------------------------------------------------------
> > --------------
> > ir. Thierry Onkelinx
> > Instituut voor natuur- en bosonderzoek / Research Institute
> > for Nature and Forest Cel biometrie, methodologie en
> > kwaliteitszorg / Section biometrics, methodology and quality
> > assurance Gaverstraat 4 9500 Geraardsbergen Belgium tel. + 32
> > 54/436 185 Thierry.Onkelinx_at_inbo.be www.inbo.be
> >
> > To call in the statistician after the experiment is done may
> > be no more than asking him to perform a post-mortem
> > examination: he may be able to say what the experiment died of.
> > ~ Sir Ronald Aylmer Fisher
> >
> > The plural of anecdote is not data.
> > ~ Roger Brinner
> >
> > The combination of some data and an aching desire for an
> > answer does not ensure that a reasonable answer can be
> > extracted from a given body of data.
> > ~ John Tukey
> >
> > -----Oorspronkelijk bericht-----
> > Van: r-help-bounces_at_r-project.org
> > [mailto:r-help-bounces_at_r-project.org] Namens Joćo Fadista
> > Verzonden: dinsdag 8 april 2008 15:18
> > Aan: r-help_at_r-project.org
> > Onderwerp: [R] permutation test assumption?
> >
> > Dear all,
> >
> > Can I do a permutation test if the number of individuals in
> > one group is much bigger than in the other group? I searched
> > the literature but I didin“t find any assumption that refers
> > to this subject for permutation tests.
> >
> >
> > Best regards
> >
> > Joćo Fadista
> > Ph.d. student
> >
> >
> >
> > UNIVERSITY OF AARHUS
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-- 
Ramon Diaz-Uriarte
Statistical Computing Team
Structural Biology and Biocomputing Programme
Spanish National Cancer Centre (CNIO)
http://ligarto.org/rdiaz

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