trouble with wilcox.test

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
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