[R] Wilcoxon signed rank test and its requirements

[Atte Tenkanen]

BTW. If there is not so weak test that would be suitable for my purpose (because of the ties and the shape of the data), could I proceed this way:

It is also worth of comparing different samples taken from the data. Since the mean and sd of the data are available, could I approximate p-values using z- or t-test, just to compare several different samples?

Atte

> 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.
> 
> -- 
> David.
> 
> >
> > 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
>