Say, I have two vector of percentages (in this particular case, percentages represent a proportion of certain cell types in blood samples). Both vectors sum up to 1.
For example, there are vectors A = [0.1, 0.15, 0.15, 0.20, 0.25, 0.15] and B = [0.05, 0.2, 0.15, 0.15, 0.2, 0.25], where A and B represent a proportion of cell type #1, etc.
What I want to do here is to find out whether the "composition" of cell types is similar between A and B. What would be the right statistical test to do this?