I have a few questions that relate to this:

- I am a bit confused why, often in research papers, the medians are reported when stating the results of a Mann Whitney Test. It seems that it's only under rare occasions when the Mann Whitney Test is actually able to compare the medians. Additionally, do researchers even check to see whether distributions are equal in the first place before saying that the test is a comparison of medians? If not, then it seems a bit unsound to report the medians.
- Is the Mann Whitney test comparing the distribution of the ranks for two groups?
- I am also a bit confused about what is stated here. The first post states that "the location-difference measure that the Mann-Whitney 'sees' is neither difference in means nor difference in medians -- it's the median of cross-group pairwise differences (the between samples quantity is the relevant estimate of the corresponding measure between populations)". Reporting Results of Mann-Whitney U Test - Means vs Medians . How exactly does "the median of cross-group pairwise differences" relate to ranks.