[R] Wilcoxon Mann-Whitney Rank Sum Test in R

Torsten Hothorn Torsten.Hothorn at rzmail.uni-erlangen.de
Wed Dec 21 08:57:15 CET 2005

On Wed, 21 Dec 2005, Peter Dalgaard wrote:

> P Ehlers <ehlers at math.ucalgary.ca> writes:
> > > so a good guess at its definition is that it is obtained from W or one
> > > of the others by subtracting the mean and dividing with the SD.
> > >
> >
> > With the SD adjusted for ties, of course. (See, e.g., Conover's book.)
> ...which is actually the exact SD, conditional on the set of tied
> ranks, not just a correction term. See my discussion with Torsten a
> month or so ago.

yes, exactly. Thanks, Peter!

The `T' values reported by functions in the `coin' package are
_standardized_ statistics. Standardization is done utilizing the
conditional expectation and conditional variance of the underlying linear
statistics as given by Strasser & Weber (1999). Note that _no_
`continuity correction' whatsoever is applied. The limit distribution is
normal (or chisq, when the test statistic is a quadratic form).

The vignette explains the theoretical framework `coin' maps into
software in more detail. It _definitively_ is worse the effort to
have a look at it. At first glance it might seem a little bit
abstract but after this you'll see how general and powerful the
tools are.

We are currently working on a manuscript showing more applications, so
watch out for the new `coin' version in a few days.



> --
>    O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
>   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
>  (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
> ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907
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