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

[P Ehlers]

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