**From:** Knut M. Wittkowski (*kmw@mail.rockefeller.edu*)

**Date:** Thu 13 May 2004 - 01:48:57 EST

**Next message:**Gabor Grothendieck: "Re: [R] How to know the row number of raw matrix after resampling?"**Previous message:**Uwe Ligges: "Re: [R] Identity matrix"**In reply to:**Margarida Júlia Rodrigues Igreja: "[R] mannwitney"

Message-id: <5.1.0.14.0.20040512110700.01df5258@imap.rockefeller.edu>

At 14:12 2004-05-12 +0100, you wrote:

*>Hi,
*

*>
*

*>I would like to do a MannWitney test.
*

*>Can anyone help me with the proper command?
*

*>
*

*>Thanks,
*

*>Margarida
*

You may use wilcox.test or qwilcox, but beware of some subtleties, which

can result in a bit of confusion (see the below comments and it's

discussion in the List in June 2003):

* > The function 'wilcox.test' in R and S gives (almost) identical results (see
*

* > below). 'qwilcox' however, does not:
*

* >
*

* > > qwilcox(p,5,5)
*

* >
*

* > p: 0.025 0.975
*

* > --------------------
*

* > R> 3 22
*

* > S> 18 37
*

* >
*

* > The S-Plus quantiles are almost correct (they are the limits of the region
*

* > of acceptance, rather than the quantiles). The description in the R help
*

file

* >
*

* > Distribution of the Wilcoxon Rank Sum Statistic
*

* >
*

* > suggests that R:qwilcox also gives quantiles for the rank sum (which the
*

* > Wilcoxon rank sum test is based on). In fact, however, it gives quantiles
*

* > for the u-statistic (which the Mann-Whitney test is based upon). While the
*

* > tests are logically equivalent, the particular test statistics
*

* >
*

* > - sum(Xi>c(X,Y)) rank sum (Wilcoxon)
*

* > - sum(Xi>c( Y)) u statistic (Mann-Whitney)
*

* >
*

* > are different (apologies for the non-standard notation). Since
*

* > "wilcox.test" relates to the rank sums in both R and S, as does qwilcox in
*

* > S, the name 'qwilcox' in R may be misleading. It might be more
*

* > appropriately be viewed as 'qmannwhitney'.
*

* >
*

* > Here are the rank sums and test statistics for two particular examples:
*

* >
*

* > > x1 <- c(1,2,3, 5,6 )
*

* > > x2 <- c( 4, 7,8,9,10)
*

* > > sum(x1)
*

* > [1] 17
*

* > > sum(x2)
*

* > [1] 38
*

* >
*

* > R> wilcox.test(x1,x2,alternative="two.sided")
*

* > Wilcoxon rank sum test: p-value = 0.03175
*

* >
*

* > > x1 <- c(1,2, 4,5,6 )
*

* > > x2 <- c( 3, 7,8,9,10)
*

* > > sum(x1)
*

* > [1] 18
*

* > > sum(x2)
*

* > [1] 37
*

* >
*

* > R> wilcox.test(x1,x2,alternative="two.sided")
*

* > Wilcoxon rank sum test: p-value = 0.05556
*

As you can see, the rank sum quantile for the .05 level (two-sided) is 18,

the result of

S> qwilcox(.025,5,5)

[1] 18

while the result of R

R> qwilcox(.025,5,5)

[1] 3

doesn't directly compare to the results of wilcox.test (both R and S).

I hope this helps.

Knut

Knut M. Wittkowski, PhD,DSc

------------------------------------------

The Rockefeller University, GCRC

Experimental Design and Biostatistics

1230 York Ave #121B, Box 322, NY,NY 10021

+1(212)327-7175, +1(212)327-8450 (Fax)

kmw@rockefeller.edu

http://www.rucares.org/clinicalresearch/dept/biometry/

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