Wilcoxon Mann-Whitney Rank Sum Test in R
Peter Dalgaard wrote:
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.
With the SD adjusted for ties, of course. (See, e.g., Conover's book.) Peter Ehlers University of Calgary