[R] The W statistic in wilcox.exact

[Christos Hatzis]

Jue,

On a second look, it appears that wilcox.test does report the
offset-adjusted statistic U, as also mentioned in the help page.

wilcox.test returns W=6 (instead of 12 as your example showed, unless
"wilcox_test" is a different function).

> wilcox.test( 1:5 ~ c(1,1,0,0,0) )$statistic  # or wilcox.test( 1:5 ~
factor(c(1,1,0,0,0)) )$statistic
W 
6  

So there does not appear to be a difference between the two methods.  Did I
miss something?

-Christos

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Christos Hatzis
Sent: Thursday, October 05, 2006 4:41 PM
To: Jue.Wang2 at sanofi-aventis.com; r-help at stat.math.ethz.ch
Subject: Re: [R] The W statistic in wilcox.exact

Probably because of the offset:

U = W - n*(n+1)/2 

In your example, W=12 (=3+4+5) as reported by wilcox.test.  The offset is 6
(=3*4/2) and therefore U=6.
I am not certain as I haven't installed the exactRankTests package, but it
seems that wilcox.exact reports U instead of W.

-Christos Hatzis

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of
Jue.Wang2 at sanofi-aventis.com
Sent: Thursday, October 05, 2006 1:35 PM
To: r-help at stat.math.ethz.ch
Subject: [R] The W statistic in wilcox.exact

Does anyone know why wilcox.exact gives W-statistic 6 instead of 12 as
indicated below.

12 is the rank sum of group 0 of x, which is the linear statistic computed
by wilcox_test.

y<-c(1,2,3,4,5)
x<-c(1,1,0,0,0)


(a) wilcox.exact

wilcox.exact(y~x)
Exact Wilcoxon rank sum test
data:  y by x
W = 6, p-value = 0.2
alternative hypothesis: true mu is not equal to 0 


(b) wilcox_test

tt<-wilcox_test(y~factor(x),distribution="exact")
statistic(tt,"linear")
   
0 12



Jue Wang, Biostatistician
Contracted Position for Preclinical & Research Biostatistics PrO Unlimited
(908) 231-3022

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