R help - Mar 2005 - wilcox.test statistics

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 is open source, so you can read the code yourself!

stats:::wilcox.test.default

-- Bert Gunter
Genentech Non-Clinical Statistics
South San Francisco, CA
 
"The business of the statistician is to catalyze the scientific learning
process."  - George E. P. Box
 
 
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Liu Ting-Yuan
> Sent: Wednesday, March 02, 2005 12:15 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] wilcox.test statistics
> 
> 
> 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 at 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
>

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 at 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 at 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