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V-value in the wilcox.test resp. wilcox.exact

3 messages · Jan M. Wiener, Peter Dalgaard, Torsten Hothorn

#
hi,
when performing a wilcox.test or a wilcox.exact i get results that looks 
like this:

wilcox.exact(x, mu=.5)
         Exact Wilcoxon signed rank test

data:  x
V = 207, p-value = 0.0006905
alternative hypothesis: true mu is not equal to 0.5


the way i understand the wilcox.test (or wilcox.exact) the V-value 
represents the summed up ranks of either the positive or negative 
differences, whichever sum is BIGGER.

to actually look up the p-value in a table (and to quote it in a 
publication) i need the T value, which to my understanding is the summed 
up ranks of either the positive or negative differences, whichever sum 
is SMALLER.

so i guess my question is: how do i get the T-value

thanks,
jan

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#
Jan Malte Wiener <jan.wiener at tuebingen.mpg.de> writes:
At least for wilcox.test, V is the sum of the *positive* ranks. The
sum of the negative ranks can be obtained by switching the sign on x
and mu. 

In the absence of ties and exact zeros, the two rank sums add up to
sum(1:N) == N*(N+1)/2

If ties are present, standard tables are wrong anyway...
#
no. wilcox.test computes the statistic along the following lines

        x <- x - mu
        ZEROES <- any(x == 0)
        if(ZEROES)
            x <- x[x != 0]
        ...
        r <- rank(abs(x))
        STATISTIC <- sum(r[x > 0])

i.e. the sum of the ranks of the absolute values of x which belong
to positive values of x.
wilcox.test computes the p-value for you, no need to look up tables.

Torsten
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