[R] mannwitney

[Knut M. Wittkowski]

At 14:12 2004-05-12 +0100, you wrote:
>Hi,
>
>I would like to do a MannWitney test.
>Can anyone help me with the proper command?
>
>Thanks,
>Margarida

You may use wilcox.test or qwilcox, but beware of some subtleties, which 
can result in a bit of confusion (see the below comments and it's 
discussion in the List in June 2003):

 > The function 'wilcox.test' in R and S gives (almost) identical results (see
 > below). 'qwilcox' however, does not:
 >
 > > qwilcox(p,5,5)
 >
 > p: 0.025 0.975
 > --------------------
 > R> 3 22
 > S> 18 37
 >
 > The S-Plus quantiles are almost correct (they are the limits of the region
 > of acceptance, rather than the quantiles). The description in the R help 
file
 >
 > Distribution of the Wilcoxon Rank Sum Statistic
 >
 > suggests that R:qwilcox also gives quantiles for the rank sum (which the
 > Wilcoxon rank sum test is based on). In fact, however, it gives quantiles
 > for the u-statistic (which the Mann-Whitney test is based upon). While the
 > tests are logically equivalent, the particular test statistics
 >
 > - sum(Xi>c(X,Y)) rank sum (Wilcoxon)
 > - sum(Xi>c( Y)) u statistic (Mann-Whitney)
 >
 > are different (apologies for the non-standard notation). Since
 > "wilcox.test" relates to the rank sums in both R and S, as does qwilcox in
 > S, the name 'qwilcox' in R may be misleading. It might be more
 > appropriately be viewed as 'qmannwhitney'.
 >
 > Here are the rank sums and test statistics for two particular examples:
 >
 > > x1 <- c(1,2,3, 5,6 )
 > > x2 <- c( 4, 7,8,9,10)
 > > sum(x1)
 > [1] 17
 > > sum(x2)
 > [1] 38
 >
 > R> wilcox.test(x1,x2,alternative="two.sided")
 > Wilcoxon rank sum test: p-value = 0.03175
 >
 > > x1 <- c(1,2, 4,5,6 )
 > > x2 <- c( 3, 7,8,9,10)
 > > sum(x1)
 > [1] 18
 > > sum(x2)
 > [1] 37
 >
 > R> wilcox.test(x1,x2,alternative="two.sided")
 > Wilcoxon rank sum test: p-value = 0.05556

As you can see, the rank sum quantile for the .05 level (two-sided) is 18,
the result of

S> qwilcox(.025,5,5)
[1] 18

while the result of R

R> qwilcox(.025,5,5)
[1] 3

doesn't directly compare to the results of wilcox.test (both R and S).

I hope this helps.
Knut


Knut M. Wittkowski, PhD,DSc
------------------------------------------
The Rockefeller University, GCRC
Experimental Design and Biostatistics
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+1(212)327-7175, +1(212)327-8450 (Fax)
kmw at rockefeller.edu
http://www.rucares.org/clinicalresearch/dept/biometry/