From: Joris Meys <jorismeys_at_gmail.com>

Date: Fri, 25 Jun 2010 00:42:39 +0200

Date: Fri, 25 Jun 2010 00:42:39 +0200

On Fri, Jun 25, 2010 at 12:17 AM, David Winsemius
<dwinsemius_at_comcast.net> wrote:

*>
*

> On Jun 24, 2010, at 6:09 PM, Joris Meys wrote:

*>
**>> I do agree that one should not trust solely on sources like wikipedia
**>> and graphpad, although they contain a lot of valuable information.
**>>
**>> This said, it is not too difficult to illustrate why, in the case of
**>> the one-sample signed rank test,
**>
**> That is a key point. I was assuming that you were using the paired sample
**> version of the WSRT and I may have been misleading the OP. For the
**> one-sample situation, the assumption of symmetry is needed but for the
**> paired sampling version of the test, the location shift becomes the tested
**> hypothesis, and no assumptions about the form of the hypothesis are made
**> except that they be the same.
*

I believe you mean the form of the distributions. The assumption that the distributions of both samples are the same (or similar, it is a robust test) implies that the differences x_i - y_i are more or less symmetrically distributed. Key point here that we're not talking about the distribution of the populations/samples (as done in the OP) but about the distribution of the difference. I may not have been clear enough on that one.

Cheers

Joris

> Any consideration of median or mean (which

*> will be the same in the case of symmetric distributions) gets lost in the
**> paired test case.
**>
**> --
**> David.
**>
**>
**>> the differences should be not to far
**>> away from symmetrical. It just needs some reflection on how the
**>> statistic is calculated. If you have an asymmetrical distribution, you
**>> have a lot of small differences with a negative sign and a lot of
**>> large differences with a positive sign if you test against the median
**>> or mean. Hence the sum of ranks for one side will be higher than for
**>> the other, leading eventually to a significant result.
**>>
**>> An extreme example :
**>>
**>>> set.seed(100)
**>>> y <- rnorm(100,1,2)^2
**>>> wilcox.test(y,mu=median(y))
**>>
**>> Wilcoxon signed rank test with continuity correction
**>>
**>> data: y
**>> V = 3240.5, p-value = 0.01396
**>> alternative hypothesis: true location is not equal to 1.829867
**>>
**>>> wilcox.test(y,mu=mean(y))
**>>
**>> Wilcoxon signed rank test with continuity correction
**>>
**>> data: y
**>> V = 1763, p-value = 0.008837
**>> alternative hypothesis: true location is not equal to 5.137409
**>>
**>> Which brings us to the question what location is actually tested in
**>> the wilcoxon test. For the measure of location to be the mean (or
**>> median), one has to assume that the distribution of the differences is
**>> rather symmetrical, which implies your data has to be distributed
**>> somewhat symmetrical. The test is robust against violations of this
**>> -implicit- assumption, but in more extreme cases skewness does matter.
**>>
**>> Cheers
**>> Joris
**>>
**>> On Thu, Jun 24, 2010 at 7:40 PM, David Winsemius <dwinsemius_at_comcast.net>
**>> wrote:
**>>>
**>>>
**>>> You are being misled. Simply finding a statement on a statistics software
**>>> website, even one as reputable as Graphpad (???), does not mean that it
**>>> is
**>>> necessarily true. My understanding (confirmed reviewing "Nonparametric
**>>> statistical methods for complete and censored data" by M. M. Desu,
**>>> Damaraju
**>>> Raghavarao, is that the Wilcoxon signed-rank test does not require that
**>>> the
**>>> underlying distributions be symmetric. The above quotation is highly
**>>> inaccurate.
**>>>
**>>> --
**>>> David.
**>>>
**>>>>
**>>
**>> --
**>> Joris Meys
**>> Statistical consultant
**>>
**>> Ghent University
**>> Faculty of Bioscience Engineering
**>> Department of Applied mathematics, biometrics and process control
**>>
**>> tel : +32 9 264 59 87
**>> Joris.Meys_at_Ugent.be
**>> -------------------------------
**>> Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php
**>
**>
*

-- Joris Meys Statistical consultant Ghent University Faculty of Bioscience Engineering Department of Applied mathematics, biometrics and process control tel : +32 9 264 59 87 Joris.Meys_at_Ugent.be ------------------------------- Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php ______________________________________________ R-help_at_r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.Received on Thu 24 Jun 2010 - 22:45:25 GMT

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