# [R] Wilcoxon signed rank test and its requirements

Atte Tenkanen attenka at utu.fi
Fri Jun 25 00:58:27 CEST 2010

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

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

Atte

> On 06/24/2010 12:40 PM, David Winsemius wrote:
> >
> > On Jun 23, 2010, at 9:58 PM, Atte Tenkanen wrote:
> >
> >>
> >> 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

```