From: David Winsemius <dwinsemius_at_comcast.net>

Date: Thu, 24 Jun 2010 18:51:43 -0400

Date: Thu, 24 Jun 2010 18:51:43 -0400

On Jun 24, 2010, at 6:42 PM, Joris Meys wrote:

> 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.
*

What I meant about different hypotheses was that in the single sample case the H0 was mean (or median) = mu_pop and in the paired two sample the H0 was mean(distr_A_i - distr_B_1) =0. And yes, I did miss the OP's point. My apologies.

-- David.Received on Thu 24 Jun 2010 - 22:54:00 GMT

>> 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

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