The Mann-Whitney U test (also known as Wilcoxon rank-sum test) allows for comparison of two groups which do not necessarily originate from normal distributions. This means that you may use this test even if the samples have a normal distribution. This is thus a good alternative to Student’s t-test when the assumption of normality might constitute a problem.
The function to use in R is
wilcox.test(x, y) where
y are the vectors containing the samples. Let’s use the same example as we have use for Student’s t-test:
W1.may15<-c(6.3,6.3,8.1,8.9,11.6,10.4,6.8) W1.may16<-c(6.9,7.7,7.9,9.1,11.3,11.8,14.2) wilcox.test(W1.may15,W1.may16)
So, the test results in a p-value greater than 0.05, thus indicating that the null hypothesis is not to be rejected. The sample means are not significantly different.