[R] wilcox.test returned estimates

[Thomas Lumley]

On Wed, 15 Feb 2006, pmt1rew at leeds.ac.uk wrote:

> Hi all,
>
> I have being using wilcox.test to test for differences between 2 independent
> samples.  I had understood the difference in location to be conventionally the
> difference in the sample medians however this is not the case when implemented
> in R.  I have tied ranks and therefore non-exact p-value and confidence
> intervals are calculated due to the normal approximation.  But what exactly is
> this normal approximation i.e. how is it involved in estimating the location
> difference?

It isn't.  The only assumption is that the distribution is the same apart 
from location in the two groups.

> Further, is it then wrong to refer to the difference in location as the
> difference between the medians?  Does anyone have a more appropriate
> description?

Well, this gets more complicated.  Since the method assumes that the 
population distributions differ only by location the population difference 
in medians is the same as the difference in means or in 16.34th 
percentile, or 42%-trimmed mean or whatever. If the assumption is not true 
then seriously weird things can happen (consider the distributions given 
by http://mathworld.wolfram.com/EfronsDice.html)

However, the estimate is not the difference in sample medians. It is the 
median pairwise difference.


 	-thomas

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle