I conducted an experiment with three treatments (A, B, control), measuring for each subject a response variable that varies between 0 and 1 (a continuous proportion). The resulting distributions of the response variable in all treatment groups appear bimodal, as can be seen in the histograms below.
I have a mechanistic hypothesis that treatments A and B should each affect bimodality, compared to the control group, in either or both of two ways: (i) increase the distance between the peaks in the group; (ii) increase the proportion of individuals in the right-side subpopulation (i.e., the one with higher values of the response variables).
I have two questions:
Is there a statistical test whether one experimental group is significantly more bimodal than another? I know that the Hartigans' Dip Test can tell me if a single group is significantly bimodal or not, but I don't think it can compare the bimodality of two groups.
Are there more refined tests for comparing specific properties of the distributions of two groups separately (specifically the distance between peaks and the relative proportions of the two subpopulations in each group)?