Mann-Whitney U test

Mann-Whitney U test is the non-parametric alternative test to the independent sample t-test.  It is a non-parametric test that is used to compare two sample means that come from the same population, and used to test whether two sample means are equal or not.  Usually, the Mann-Whitney U test is used when the data is ordinal or when the assumptions of the t-test are not met.
Mann-Whitney U test is a non-parametric test, so it does not assume any assumptions related to the distribution of scores.  There are, however, some assumptions that are assumed
1. The sample drawn from the population is random.
2. Independence within the samples and mutual independence is assumed.  That means that an observation is in one group or the other (it cannot be in both).
3. Ordinal measurement scale is assumed.

Where:
U=Mann-Whitney U test
N1 = sample size one
N2= Sample size two
Ri = Rank of the sample size
※Mann Whitney U test is also called the Mann–Whitney–Wilcoxon (MWW), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test

Use of Mann-Whitney

Mann-Whitney U test is used for every field, but is frequently used in psychology, healthcare, nursing, business, and many other disciplines.  For example, in psychology, it is used to compare attitude or behavior, etc.  In medicine, it is used to know the effect of two medicines and whether they are equal or not.  It is also used to know whether or not a particular medicine cures the ailment or not.  In business, it can be used to know the preferences of different people and it can be used to see if that changes depending on location.
(from here)

在教材里面，这个Mann Whitney U test是用来比较两组相互独立的样本的中间值的(median)。
Mann-Whitney test in R
wilcox.test