R help - Sep 2009 - Equivalence of Mann-Whitney test and Kruskal-Wallis test with k=2

Hi all,

The Kruskal-Wallis test is a generalization of the two-sample Mann-Whitney
test to *k* samples.  That being the case, the Kruskal-Wallis test with *k*=2
should give an identical p-value to the Mann-Whitney test, should it not?

x1<-c(1:5)
x2<-c(6,8,9,11)
a<-wilcox.test(x1,x2,paired=FALSE)
b<-kruskal.test(list(x1,x2),paired=FALSE)
a$p.value
[1] 0.01587302
b$p.value
[1] 0.01430588

The p-values are slightly different (note that there are no ties in the
data, so computed p-values should be exact).

Can anyone explain the discrepancy?  It's been awhile since I studied
nonparametric stats and this one has me scratching my head.

Many thanks!
Tom

	[[alternative HTML version deleted]]

Thomas Farrar wrote:
> Hi all,
> 
> The Kruskal-Wallis test is a generalization of the two-sample Mann-Whitney
> test to *k* samples.  That being the case, the Kruskal-Wallis test with
*k*=2
> should give an identical p-value to the Mann-Whitney test, should it not?
> 
> x1<-c(1:5)
> x2<-c(6,8,9,11)
> a<-wilcox.test(x1,x2,paired=FALSE)
> b<-kruskal.test(list(x1,x2),paired=FALSE)
> a$p.value
> [1] 0.01587302
> b$p.value
> [1] 0.01430588
> 
> The p-values are slightly different (note that there are no ties in the
> data, so computed p-values should be exact).
> 
> Can anyone explain the discrepancy?  It's been awhile since I studied
> nonparametric stats and this one has me scratching my head.
> 
> Many thanks!
> Tom
> 
The continuity correction? It is true by default for wilcox.test and is 
not apparent in the help for kruskal.test.

David Scott

-- 
_________________________________________________________________
David Scott	Department of Statistics
		The University of Auckland, PB 92019
		Auckland 1142,    NEW ZEALAND
Phone: +64 9 923 5055, or +64 9 373 7599 ext 85055
Email:	d.scott at auckland.ac.nz,  Fax: +64 9 373 7018

Director of Consulting, Department of Statistics