[R] Interpreting the result of a Wilcoxon (Mann-Whitney U) test

[Filipe Correia]

Hello everyone,

I'm having some trouble interpreting the results of a Wilcoxon
(Mann-Whitney U) test. Hope you can help.

This is the R script that I am running:

a <- c(1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 5, 1, 1, 1, 3, 1, 1,
1, 1, 1, 1, 3, 1, 1)
b <- c(1, 2, 1, 1, 2, 3, 2, 2, 1, 2, 1, 1, 1, 2)
wilcox.test(a, b, alternative="t", mu=0, exact=FALSE, paired=FALSE)  #1st
wilcox.test(a, b, alternative="l", mu=0, exact=FALSE, paired=FALSE)  #2nd
wilcox.test(a, b, alternative="g", mu=0, exact=FALSE, paired=FALSE)  #3rd

... and it's returning:

Wilcoxon rank sum test with continuity correction data:  a and b
W = 145, p-value = 0.08969
alternative hypothesis: true location shift is not equal to 0

Wilcoxon rank sum test with continuity correction data:  a and b
W = 145, p-value = 0.04485
alternative hypothesis: true location shift is less than 0

Wilcoxon rank sum test with continuity correction data:  a and b
W = 145, p-value = 0.9582
alternative hypothesis: true location shift is greater than 0

The null hypothesis is that the populations are equivalent (mu=0). The
alternative hypothesis are that they differ, with the 2nd and 3rd runs
of the test above considering respectively that a<b and b>a. Plus, I'm
considering an alfa of 0.05.

My issue is that from the first run I could not conclude that there
was a difference between the two populations (0.08969>0.05), but the
second run leads me to think that a<b (because 0.04485<0.05).

Am I misinterpreting the results?

Thanks!

Filipe