[R] Wilcoxon signed rank test and its requirements

David Winsemius dwinsemius at comcast.net
Fri Jun 25 05:52:45 CEST 2010

On Jun 24, 2010, at 6:58 PM, Atte Tenkanen wrote:

> Is there anything for me?
> There is a lot of data, n=2418, but there are also a lot of ties.
> My sample n≈250-300

I do not understand why there should be so many ties. You have not  
described the measurement process or units. ( ... although you offer a  
glipmse without much background  later.)

> i would like to test, whether the mean of the sample differ  
> significantly from the population mean.

Why? What is the purpose of this investigation? Why should the mean of  
a sample be that important?

> The histogram of the population looks like in attached histogram,  
> what test should I use? No choices?
> This distribution comes from a musical piece and the values are  
> 'tonal distances'.
> http://users.utu.fi/attenka/Hist.png

That picture does not offer much insidght into the features of that  
measurement. It appears to have much more structure than I would  
expect for a sample from a smooth unimodal underlying population.


> Atte
>> On 06/24/2010 12:40 PM, David Winsemius wrote:
>>> 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.
>> To add to what David and others have said, look at the kernel that  
>> the
>> U-statistic associated with the WSR test uses: the indicator (0/1) of
>> xi
>> + xj > 0.  So WSR tests H0:p=0.5 where p = the probability that the
>> average of a randomly chosen pair of values is positive.  [If there
>> are
>> ties this probably needs to be worded as P[xi + xj > 0] = P[xi + xj <
>> 0], i neq j.
>> Frank
>> -- 
>> Frank E Harrell Jr   Professor and Chairman        School of Medicine
>>                      Department of Biostatistics   Vanderbilt  
>> University

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