From: Christoph Buser <buser_at_stat.math.ethz.ch>

Date: Thu 03 Mar 2005 - 22:08:24 EST

Wilcoxon rank sum test

Christoph Buser <buser@stat.math.ethz.ch> Seminar fuer Statistik, LEO C11

http://stat.ethz.ch/~buser/

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Thu Mar 03 22:59:28 2005

Date: Thu 03 Mar 2005 - 22:08:24 EST

Hi,

a value of 0 for the test statistic is possible. The test
statistic is not just the sum of ranks, but this sum - n*(n+1)/2,
where n is the number of observations of the group the rank sum
is build.

This statistic is equivalent to the ranks sums, since it
differs only about a constant, which depends on the number of
observations.

Look at the following situation

> x <- 1:10 > y <- 11:20 > wilcox.test(x,y)

Wilcoxon rank sum test

data: x and y

W = 0, p-value = 1.083e-05

alternative hypothesis: true mu is not equal to 0

When every observation of group1 is smaller than those of group2
the rank sum of the smaller group is

sum(1:n1) = sum(1:10) = 10*(10+1)/2 = n1*(n1+1)/2
If you compare this to the test statistics, you'll observe that
in this case the test statistic is 0.

Regards,

Christoph Buser

Christoph Buser <buser@stat.math.ethz.ch> Seminar fuer Statistik, LEO C11

ETH (Federal Inst. Technology) 8092 Zurich SWITZERLAND phone: x-41-1-632-5414 fax: 632-1228

http://stat.ethz.ch/~buser/

Liu Ting-Yuan writes:

* >
** > Hi,
** >
*

> Could anyone provide the formula of the statistics which the wilcox.test

* > used for the two-sample rank-sum test? I got some statistics of 0 values,
** > but it is impossible to have 0 "rank-sum". Does the function use the
** > Mann-Whitney U test statistics? Thanks.
** >
** > Ting-Yuan Liu
** >
** > ______________________________________________
** > R-help@stat.math.ethz.ch mailing list
** > https://stat.ethz.ch/mailman/listinfo/r-help
** > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
*

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Thu Mar 03 22:59:28 2005

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