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 Different ways to calculate the test statistic for the Wilcoxon rank sum test