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

From: Peter Dalgaard <>
Date: Wed 21 Dec 2005 - 09:02:31 EST

Bob Green <> 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             ุster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
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Received on Wed Dec 21 09:24:48 2005

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