# Re: [R] Wilcoxon signed rank test and its requirements

From: Frank E Harrell Jr <f.harrell_at_vanderbilt.edu>
Date: Fri, 25 Jun 2010 12:09:49 -0500

You still are stating the effect of the central limit theorem incorrectly. Please see my previous note.

Frank

On 06/25/2010 10:27 AM, Joris Meys wrote:
> 2010/6/25 Frank E Harrell Jr<f.harrell@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¡Ö250-300
>>>
>>> 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
>>
```

>
>
>
```--
Frank E Harrell Jr   Professor and Chairman        School of Medicine
Department of Biostatistics   Vanderbilt University

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Received on Fri 25 Jun 2010 - 17:12:11 GMT

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