Wilcoxon Rank Sum Test

The Wilcoxon Rank Sum Test, also known as the Mann-Whitney U Test, is a is a non-parametric statistical test used to compare two samples or groups

It "assesses whether two sampled groups are likely to derive from the same population, and essentially asks; do these two populations have the same shape with regards to their data? In other words, we want evidence as to whether the groups are drawn from populations with different levels of a variable of interest. It follows that the hypotheses in a Mann-Whitney U Test are:

The null hypothesis (H0) is that the two populations are equal.
The alternative hypothesis (H1) is that the two populations are not equal."

https://www.technologynetworks.com/informatics/articles/mann-whitney-u-test-assumptions-and-example-363425

Application example:

Consider a randomized controlled trial evaluating a new anti-retroviral therapy for HIV. A pilot trial randomly assigned participants to either the treated or untreated groups (N=14). We want to assess the viral load (quantity of virus per milliliter of blood) in the treated versus the untreated groups.

View the complete example including tables and formulas used to derive a conclusion.