I have a situation like the following:
5 distributions A, B, C, D, E of unknown type from which I can take samples to estimate the mean.
I apply an intervention or treatment to all of the distributions.
I take another set of samples from each of these distributions and again estimate the mean.
Effectively, the distributions are paired, but the samples within the distribution aren't necessarily. How can I test for statistical significance of the treatment effect if the samples aren't paired? If they are, is there a different approach beyond combining all of the samples into a single large distribution and performing e.g. a paired t test?