I have a continuously variable output (diffusivities) that I have measured from two different populations (say "Case 1" and "Case 2"), and I am trying to see if the two populations are different. The trouble is, each population has two known subpopulations ("ventral" and "dorsal"), which we know have different diffusivities between them. So if I combine the data, Case 1 and Case 2 both have bimodal distributions. I would like to know if I can state that the differences behind the two Cases are driving differences in diffusivities as a whole.
If you would like, I can post more details about the actual problem, but the simplest analogy I could come up with was something like asking whether two sheep species have different weights. Both species are sexually dimorphic, so we know for sure that, on average, males weigh significantly more than females. I know we could test males and females separately, but I would like to see if species A weighs more than species B in some sort of "combined" sense. Maybe it's because I'd like to test whether genetic differences between the two species are the culprit, or maybe I need to increase the power of the test, but for whatever reason I would like to combine the two data sets and get a p-value for the combined population.
Would there be a simple (or even not-so-simple) way of doing that?