[R] Wilcoxon signed rank test and its requirements

[Atte Tenkanen]

> On Jun 23, 2010, at 9:58 PM, Atte Tenkanen wrote:
> 
> > Thanks. What I have had to ask is that
> >
> > how do you test that the data is symmetric enough?
> > If it is not, is it ok to use some data transformation?
> >
> > when it is said:
> >
> > "The Wilcoxon signed rank test does not assume that the data are  
> > sampled from a Gaussian distribution. However it does assume that  
> > the data are distributed symmetrically around the median. If the  
> > distribution is asymmetrical, the P value will not tell you much  
> > about whether the median is different than the hypothetical value."
> 
> 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.

Thanks. Unfortunately, I can't follow the reference at all, but I read this in that way that I can be carefree as far as the underlying distribution is concerned?

Is there any other authoritative reference where that is just stated in a way "test does not require that the underlying distributions be   symmetric or normal".

Atte


> >
> >> On Wed, Jun 23, 2010 at 10:27 PM, Atte Tenkanen <attenka at utu.fi>  
> >> wrote:
> >>> Hi all,
> >>>
> >>> I have a distribution, and take a sample of it. Then I compare that
> >> sample with the mean of the population like here in "Wilcoxon signed
> >> rank test with continuity correction":
> >>>
> >>>> wilcox.test(Sample,mu=mean(All), alt="two.sided")
> >>>
> >>>        Wilcoxon signed rank test with continuity correction
> >>>
> >>> data:  AlphaNoteOnsetDists
> >>> V = 63855, p-value = 0.0002093
> >>> alternative hypothesis: true location is not equal to 0.4115136
> >>>
> >>>> wilcox.test(Sample,mu=mean(All), alt = "greater")
> >>>
> >>>        Wilcoxon signed rank test with continuity correction
> >>>
> >>> data:  AlphaNoteOnsetDists
> >>> V = 63855, p-value = 0.0001047
> >>> alternative hypothesis: true location is greater than 0.4115136
> >>>
> >>> What assumptions are needed for the population?
> >>
> >> wikipedia says:
> >> "The Wilcoxon signed-rank test is a _non-parametric_ statistical
> >> hypothesis test for... "
> >> it also talks about the assumptions.
> >>
> >>> What can we say according these results?
> >>> p-value for the "less" is 0.999.
> >>
> >> That the p-value for less and greater seem to sum up to one, and that
> >> the p-value of greater is half of that for two-sided. You shouldn't
> >> ask what we can say. You should ask yourself "What was the question
> >> and is this test giving me an answer on that question?"
> >>
> >> Cheers
> >> Joris
> >>
> >> -- 
> >> 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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