# [R] Wilcoxon signed rank test and its requirements

Joris Meys jorismeys at gmail.com
Fri Jun 25 17:27:09 CEST 2010

```2010/6/25 Frank E Harrell Jr <f.harrell at vanderbilt.edu>:
> The central limit theorem doesn't help.  It just addresses type I error,
> not power.
>
> Frank

I don't think I stated otherwise. I am aware of the fact that the
wilcoxon has an Asymptotic Relative Efficiency greater than 1 compared
to the t-test in case of skewed distributions. Apologies if I caused
more confusion.

The "problem" with the wilcoxon is twofold as far as I understood this
data correctly :
- there are quite some ties
- the wilcoxon assumes under the null that the distributions are the
same, not only the location. The influence of unequal variances and/or
shapes of the distribution is enhanced in the case of unequal sample
sizes.

The central limit theory makes that :
- the t-test will do correct inference in the presence of ties
- unequal variances can be taken into account using the modified
t-test, both in the case of equal and unequal sample sizes

For these reasons, I would personally use the t-test for comparing two
samples from the described population. Your mileage may vary.

Cheers
Joris

>
> On 06/25/2010 04:29 AM, Joris Meys wrote:
>> As a remark on your histogram : use less breaks! This histogram tells
>> you nothing. An interesting function is ?density , eg :
>>
>> x<-rnorm(250)
>> hist(x,freq=F)
>> lines(density(x),col="red")
>>
>> See also this ppt, a very nice and short introduction to graphics in R :
>> http://csg.sph.umich.edu/docs/R/graphics-1.pdf
>>
>> 2010/6/25 Atte Tenkanen<attenka at utu.fi>:
>>> 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
>>
>> You should think about the central limit theorem. Actually, you can
>> just use a t-test to compare means, as with those sample sizes the
>> mean is almost certainly normally distributed.
>>>
>>> i would like to test, whether the mean of the sample differ significantly from the population mean.
>>>
>> According to probability theory, this will be in 5% of the cases if
>> you repeat your sampling infinitly. But as David asked: why on earth
>> do you want to test that?
>>
>> cheers
>> Joris
>>
>
>
> --
> Frank E Harrell Jr   Professor and Chairman        School of Medicine
>                     Department of Biostatistics   Vanderbilt University
>

--
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
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