Hypothesis testing for multiple distributions 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?
EDIT
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.
 A: I think your confusion lies in framing your problem incorrectly. Think less in terms of your raw data and more in terms of the entities that characterize your study. 
You have two populations. These populations are defined by some features. You want to know if these populations are different. 
Let's consider first a simpler case where each population is defined by only one feature. The obvious choice here would be a t-test. Now let's consider the choice where each population is defined by two features. Each individual in your dataset is a point in two dimensional space: you don't have "two distributions" for each individual, the individuals are being drawn from a two-dimensional multivariate distribution. Similarly, in your current problem setup, I contend that you are looking for a test to compare the means of two 15-dimensional multivariate distributions. I believe the appropriate test here is the two-sample Hotelling's T-square test, which is the multivariate analog of the two-sample Student's t-test.
If you are unsure, consider comparing your experiment with the example described here.
A: For a simple test of the difference between populations I would consider using the mean for each individual, and a Mann-Whitney U or t-test to test for a difference between the 15 individuals in each population (since you are only comparing a single variable). You could also do glm where you include 'individual' as a random effect, and test for the fixed effect of 'population'. However, when looking at your plot, it looks like you are mostly interested in the difference in variance between populations. Have the measurements been standardized within individuals or do all hover around zero as raw data? To test for a difference in variance between populations (using means of individuals) you can use the Levene's test.
However, all this depends on whether the multiple measurements (the time series) are only used to account for measurment error or if they have a specific purpose (e.g. track a change over time during an experiment). For instance, if you want to model how the difference between populations changes over time you need to take the autocorrelation between time points into account. So the question is; why have you taken multiple measurements for each individual?
Basic code for the Levene's test (on means of individuals) would be:
library(car)
leveneTest(indmean ~ population, data= datafile,center="median")

For a preliminary/simple test of difference in individual variance between groups you could use the same test, but with individual variance as response. However, if the main aim is to model within-individual variance and how this differs between groups, a hierarchical random effects model is probably more suitable (nested as observations within individuals within groups).
