On Fri, Jun 25, 2010 at 12:17 AM, David Winsemius <dwinsem...@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 <dwinsem...@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.m...@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.m...@ugent.be ------------------------------- Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php ______________________________________________ R-help@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.
