meaning V value, wilcoxen signed rank test

Question

I have a question about my results of the Wilcoxon signed rank test:

My data consists of a trial with 2 groups (paired) in which a treatment was used. The results were scored in %. Groups consist of 131 people.

When I run the test in R, I got the following result:

wilcox.test(no.treatment, with.treatment, paired=T) 
# Wilcoxon signed rank test with continuity correction 
# data:  no.treatment and with.treatment V = 3832, p-value = 0.7958
# alternative hypothesis: true location shift is not equal to 0

I am wondering what the V value means. I read somewhere that it has something to do with the number of positive scores (?), but I am wondering if it could tell me anything about the data and interpretation?

Answer 1

I'll give a little bit of background before answering your question.

The Wilcoxon signed rank sum test compares two values between the same N people (here 131), like for example blood values were measured for 131 people at two time points. The purpose of the test is to see whether the blood values have changed.

The V-statistic you are getting does not have a direct interpretation. This value is based on the pairwise difference between the individuals in your two groups. It is a value for a variable, that is supposed to follow a certain probability distribution. Intuitively speaking, you can say that the larger the value for V, the larger the difference between the two groups you sampled.

As always in hypothesis testing, you (well, the wilcox.test function) will calculate the probability that the value (V) of that variable is equal to 3832 or larger prob('observing a value of 3832 or larger, when the groups are actually the same')

If there is really no difference between the two groups, the value for V will be 'close to zero'. Whether the value V you see is 'close to zero' depends on the probability distribution. The probability distribution is not straightforward for this variable, but luckily that doesn't matter since wilcoxon knows the distribution and calculates the probability for you (0.7958).

In short

Your groups do not significantly differ and V doesn't have a clear interpretation.