I have results from the same test applied to two independent samples: x <- c(17, 12, 13, 16, 9, 19, 21, 12, 18, 17) y <- c(10, 6, 15, 9, 8, 11, 8, 16, 13, 7, 5, 14) And I want to compute a Wilcoxon rank sum test. When I calculate the statistic $T_{W}$ by hand, I get: $$ T_{W}=\sum\text{rank}(X_{i}) = 156.5 $$ When I let R perform a `wilcox.test(x, y, correct = F)`, I get: W = 101.5 Why is that? Shouldn't the statistic $W^{+}$ only be returned when I perform a *signed* rank test with `paired = T`? Or do I misunderstand the rank sum test? **How can I tell R to output $T_{W}$** * * * As part of the test results, not through something like: dat <- data.frame(v = c(x, y), s = factor(rep(c("x", "y"), c(10, 12)))) dat$r <- rank(dat$v) T.W <- sum(dat$r[dat$s == "x"]) * * * *I asked a follow up question about the meaning of the http://stats.stackexchange.com/questions/65875/different-ways-to-calculate-the-test-statistic-for-the-wilcoxon-rank-sum-test*