[R] Wilcoxon Mann-Whitney Rank Sum Test in R

Peter Dalgaard p.dalgaard at biostat.ku.dk
Tue Dec 20 23:02:31 CET 2005

Bob Green <bgreen at dyson.brisnet.org.au> writes:

> An earlier post had posed the question: "Does anybody know what is relation 
> between 'T' value calculated by 'wilcox_test' function (coin package) and 
> more common 'W' value?"
> I found the question interesting and ran the commands in R and SPSS. The W 
> reported by R did not seem to correspond to either   Mann-Whitney U, 
> Wilcoxon W or the Z which I have more commonly used. Correction for ties 
> may have affected my results.
> Can anyone else explain what the reported W is and the relation to the 
> reported T?

Well, it's open source... You could just go check.

W is the sum of the ranks in the first group, minus the minimum value
it can attain, namely sum(1:n1) == n1*(n1+1)/2. In the tied cases, the
actual minimum could be larger.

The T would seem to be asymptotically normal 

> wilcox_test(pd ~ age, data = water_transfer,distribution="asymp")

        Asymptotic Wilcoxon Mann-Whitney Rank Sum Test

data:  pd by groups 12-26 Weeks, At term
T = -1.2247, p-value = 0.2207
alternative hypothesis: true mu is not equal to 0

> pnorm(-1.2247)*2
[1] 0.2206883

so a good guess at its definition is that it is obtained from W or one
of the others by subtracting the mean and dividing with the SD.

   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907

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