What is mean rank? I am a student and I am doing a project that consists of calculating Mann Whitney U test. I would like to know the definition of mean rank that is calculated with this analysis. Also, I would like to know what is the difference between median and mean rank?
 A: Given a column of data that looks like this:
20
23
21
25
20

You need to rank the column smallest to largest and then calculate rank by noting the position in a second column:
20  1.5
20  1.5
21  3
23  4
25  5

If the data have ties (like the two 20s here in first and second place), averaged position is used.
Mean rank will be the arithmetic average of the positions in the list: $$\frac{1.5+1.5+3+4+5}{5}=3$$
When there is an odd number of rows, the median will be the middle value of the original data after it is ranked. If there is an even number of rows, you take the average of the two values in the middle. Here the median is 21.
The median rank will be the same calculation, but for the column noting the position. Here it is 3, same as the mean.
Usually, the mean rank and the median rank will be different.
A: When using the Mann-Whitney U test, if two population samples have similar shapes the result of the test can be used to infer whether two population medians differ or not. But when the shapes are different, the result only indicates whether the mean rank of two populations varies.
