[R] wilcox.test returned estimates

[Torsten Hothorn]

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?

the reference distribution is not involved in _estimating_ the difference 
in location. `wilcox.test' implements the Hodges-Lehmann estimator:

from `stats/R/wilcox.test.R'

                 ## Exact confidence interval for the location parameter
                 ## mean(x) - mean(y) in the two-sample case (cf. the
                 ## one-sample case).
                 alpha <- 1 - conf.level
                 diffs <- sort(outer(x, y, "-"))
                 ...
                 ESTIMATE <- median(diffs)
                 names(ESTIMATE) <- "difference in location"

which simply is the median of all pairwise differences.

However, the usual normal approximation to the exact conditional 
distribution (in case of ties) of the Wilcoxon-Mann-Whitney statistic 
(see Hajek, Sidak, Sen for example) is involved in computing a confidence 
interval for the difference in location.

Hope that helps,

Torsten

>
> 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?
>
> Thanks
>
> Rebecca
>
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