Re: [R] trouble with wilcox.test

From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>
Date: Thu 18 Aug 2005 - 16:45:48 EST

On Wed, 17 Aug 2005, Greg Hather wrote:

> I'm having trouble with the wilcox.test command in R.

Are you sure it is not the concepts that are giving 'trouble'? What real problem are you trying to solve here?

> To demonstrate the anomalous behavior of wilcox.test, consider
>
>> wilcox.test(c(1.5,5.5), c(1:10000), exact = F)$p.value
> [1] 0.01438390
>> wilcox.test(c(1.5,5.5), c(1:10000), exact = T)$p.value
> [1] 6.39808e-07 (this calculation takes noticeably longer).
>> wilcox.test(c(1.5,5.5), c(1:20000), exact = T)$p.value
> (R closes/crashes)
>
> I believe that wilcox.test(c(1.5,5.5), c(1:10000), exact = F)$p.value
> yields a bad result because of the normal approximation which R uses
> when exact = F.

Expecting an approximation to be good in the tail for m=2 is pretty unrealistic. But then so is believing the null hypothesis of a common *continuous* distribution. Why worry about the distribution under a hypothesis that is patently false?

People often refer to this class of tests as `distribution-free', but they are not. The Wilcoxon test is designed for power against shift alternatives, but here there appears to be a very large difference in spread. So

> wilcox.test(5000+c(1.5,5.5), c(1:10000), exact = T)$p.value
[1] 0.9989005

even though the two samples differ in important ways.

> Any suggestions for how to compute
> wilcox.test(c(1.5,5.5), c(1:20000), exact = T)$p.value?

I get (current R 2.1.1 on Linux)

> wilcox.test(c(1.5,5.5), c(1:20000), exact = T)$p.value
[1] 1.59976e-07

and no crash. So the suggestion is to use a machine adequate to the task, and that probably means an OS with adequate stack size.

> [[alternative HTML version deleted]]

> PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html

Please do heed it. What version of R and what machine is this? And do take note of the request about HTML mail.

-- 
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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Received on Thu Aug 18 16:52:05 2005

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