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