[R] Wilcoxon signed rank test and its requirements

[David Winsemius]

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.

>
>> 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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