[R] trouble with wilcox.test

[Prof Brian Ripley]

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.

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-- 
Brian D. Ripley,                  ripley at 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