[R] Confidence interval in the Wilcoxon exact test

[Thomas Lumley]

On Fri, 29 Sep 2006, Jue.Wang2 at sanofi-aventis.com wrote:

> Hi,
>
> Two functions wilcox.exact and wilcox_test give slightly different 
> confidence intervals of the difference of the medians: for example
>
> y<-c(0,0,1.081,0.594,0,0.769,0,0.009,0,0,0.798,0.405,0.498,0.946,1.35,1.149,0.528)
> x<-c(rep(1,10),rep(2,7))
>
> aa<-wilcox.exact(y~x,conf.int=TRUE)
> bb<-wilcox_test(y~factor(x),distribution="exact",conf.int=TRUE)
>
> aa
> bb
>
> Does anyone know why?
>

The help for wilcox.test says
      'wilcox.exact' in 'exactRankTests' covers much of the same ground,
      but also produces exact p-values in the presence of ties.
so that is probably the explanation.

However, since your x and y can't really have come from distributions 
differing only by a location shift, the confidence interval isn't valid 
anyway (and the test is valid only to reject the strong null hypothesis 
that the distributions are the same, not anything about medians)

 	-thomas