[R] Wilcoxon Mann-Whitney Rank Sum Test in R
P Ehlers
ehlers at math.ucalgary.ca
Wed Dec 21 00:20:52 CET 2005
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
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