On Tue, 10 Jun 2003, Knut M. Wittkowski wrote: > 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,
That is not true. You did not tell us the whole story: `wilcox.test' in S-PLUS 2000 reports a statistic of `W = 17' for your example below whereas R says R> wilcox.test(x1,x2,alternative="two.sided") Wilcoxon rank sum test data: x1 and x2 W = 2, p-value = 0.03175 alternative hypothesis: true mu is not equal to 0 and as one can find out easily, `wilcox.test' computes the statistic as STATISTIC <- sum(r[seq(along = x)]) - n.x * (n.x + 1) / 2 So both R and S are consistent and ?qwilcox will tell you what exactly is meant by `Wilcoxon rank sum': This distribution is obtained as follows. Let `x' and `y' be two random, independent samples of size `m' and `n'. Then the Wilcoxon rank sum statistic is the number of all pairs `(x[i], y[j])' for which `y[j]' is not greater than `x[i]'. This statistic takes values between `0' and `m * n', and its mean and variance are `m * n / 2' and `m * n * (m + n + 1) / 12', respectively. Best, Torsten > 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) > [EMAIL PROTECTED] > http://www.rucares.org/statist/ > > ______________________________________________ > [EMAIL PROTECTED] mailing list > https://www.stat.math.ethz.ch/mailman/listinfo/r-help > > ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help