Re: [R] wilcox.test returned estimates

From: Thomas Lumley <tlumley_at_u.washington.edu>
Date: Thu 16 Feb 2006 - 07:54:44 EST

On Wed, 15 Feb 2006, pmt1rew@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@u.washington.edu	University of Washington, Seattle

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