I have a set of distributions (histograms) relating to data sampled from two different populations. Within each population I have $n=15$ distributions. I am looking for a statistical test that will tell me whether the two populations are statistically different, or not, based on the distributions within them.
Most tests I have looked at (e.g. Mann-Whitney U, Wilcoxon) seem to compare two samples. However, since I have 15 samples in each population, I am confused as to whether these tests can be applied in this instance. Is it possible to just pool the data so that I have one aggregated distribution for each population, then run a test on the result?
Here is a selection of 5 distributions (histograms) from each population, plotted on the same axes:
I want to know if there is a statistical difference between the sets (black and orange) of distributions.