Given this example
#start code
a<-c(0,70,50,100,70,650,1300,6900,1780,4930,1120,700,190,940,
760,100,300,36270,5610,249680,1760,4040,164890,17230,75140,1870,22380,5890,2430)
b<-c(0,0,10,30,50,440,1000,140,70,90,60,60,20,90,180,30,90,
3220,490,20790,290,740,5350,940,3910,0,640,850,260)
wilcox.test(a, b, paired=FALSE)
#sum of rank for first sample
sum.rank.a <- sum(rank(c(a,b))[1:29]) #sum of ranks assigned to the group a
W1<- sum.rank.a - (length(a)*(length(a)+1)) / 2
W1
U1 <- length(a)*length(b)/2-W1
U1
#sum of ranks for second sample
sum.rank.b <-sum(rank(c(a,b))[30:58]) #sum of ranks assigned to the group b
W2 <- sum.rank.b - (length(b)*(length(b)+1)) / 2
W2
U2 <- length(a)*length(b)/2-W2
U2
#end code
And given the fact that:
- in the note of R Wilcox.test is clearly stated: “ The literature is not
unanimous about the definitions of the Wilcoxon rank sum and Mann-Whitney
tests. The two most common definitions correspond to the sum of the ranks of
the first sample with the minimum value subtracted or not. R subtracts [….],
giving a value which is larger by m(m+1)/2 for a first sample of size m”
- as result of the same test performed with different stat packages (i.e.
STATISTICA and PAST) I’ve got an U value of 200.5 as in W2 (see my script)
with the same p-value
What can I conclude regarding STATISTICA and PAST packages?... are they
giving W2 (see my script) instead of U?
A crucial point is that the variant of the algorithm used for computation by
the packages is very rarely indicated in the output or documented in the
help facility and the manuals.
See also this link (I’ve found after a long meandering on the web) about the
comparison of “wilcoxon mann whitney” u test outcomes from different stat
packages:
http://www.jstor.org/discover/10.2307/2685616?uid=3738296&uid=2129&uid=2&uid=70&uid=4&sid=47699045750617
Any of you have faced the same type of issues? Or am I completely wrong?
maxbre
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