Here it is assumed that the distribution of Group 1 and that of Group 2 share the same shape with possible shift, but not necessarily normally distributed. The Wilcoxon rank sum test is based on ranks--the rank 1 is assigned to the smallest measurement in both groups, and 2 to the second smallest, and so on. Recall that the validity of t-test is based on the ``normality of population distributions,'' and that it requires that either sample distributions are approximately normal, or the sample sizes are appropriately large ( ). Since a normal distribution is ``parametric,'' the rank sum test procedure is referred as ``nonparametric,'' free from the assumption of normal distribution.
The null hypothesis is stated as ``the distributions from two groups are identical,'' and the test will determine whether it is rejected in favor of the following alternative hypothesis.
It produces the estimate ``estimate.shift'' and the confidence interval ``(lower.bound,upper.bound)'' for the shift (the difference of locations) with confidence interval. The value p.value indicates the significance of the test: If p-value < , it suggest evidence against the null hypothesis in favor of the alternative hypothesis.
Here the estimate ``estimate.shift'' is calculated from the sample median of the difference between in Group 1 and in Group 2. It is called the Hodges-Lehmann estimator.