MATLAB: When using the “ranksum” function, how can I differentiate bewteen the two options of getting a low p-value

Question

Say I have two vectors- A and B. If I get a low p-value, I would like to check whether this low p-value stands for high median of B compared to A, instead of just different medians (that is, either the median of B is higher than the median of A, or vise versa).

For example:

A=[120 10 201 20 30 12 30 10 2 2 3 5 1]
B=[140 400 120 2000 30 40 2000 1000 1000]

I get a p-value of 7.2251e-004.

But if

B=[1 0 0 0 0 0 0 0 0 0 0 0 0]

I also get a low p-value (6.4360e-006).

I would like to get only low p-values when B median is higher then A median. Since I have many calculations, I need it to be automatically in the code, instead of checking every pair of vectors. Do you have any idea how to do that?

Thanks, Michal

Answer 1

Both ‘one-sided’ (that one median is greater than or less than the other) and ‘two-sided’ (that the medians are different) options are possible. See Item #4 under Assumptions and formal statement of hypotheses in the Wikipedia article on the Mann–Whitney U. There is also an excellent discussion of this on page 3 of The Wilcoxon Rank-Sum Test.

According the the documentation, ranksum returns the two-sided p-value, so make the appropriate calculation to get the one-sided p-value.