[R] qwilcox

[Knut M. Wittkowski]

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

I originally wanted to ask a questions, but then I found the answer. Given 
the confusion I run into, I wonder if this experience is worth reporting.

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. How about renaming it to 
'qmannwhitney' instead and adding 'qwilcoxon' for a function that 
corresponds to S:qwilcox?

 > 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

R> wilcox.exact(x1,x2,alternative="two.sided")
         Exact Wilcoxon rank sum test: p-value = 0.03175

S> wilcox.test(x1,x2,alternative="two.sided")
         Exact Wilcoxon rank-sum test: p-value = 0.0317

 > 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

R> wilcox.exact(x1,x2,alternative="two.sided")
         Exact Wilcoxon rank sum test: p-value = 0.05556

S> wilcox.test(x1,x2,alternative="two.sided")
         Exact Wilcoxon rank sum test: p-value = 0.0556


Knut M. Wittkowski, PhD,DSc
------------------------------------------
The Rockefeller University, GCRC
1230 York Ave #121B, Box 322, NY,NY 10021
+1(212)327-7175, +1(212)327-8450 (Fax)
kmw at rockefeller.edu
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