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

From: P Ehlers <ehlers_at_math.ucalgary.ca>
Date: Wed 21 Dec 2005 - 10:20:52 EST

Peter Dalgaard wrote:
> Bob Green <bgreen@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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