# Testing for difference in bimodality between experimental groups

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:

1. 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.

2. 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)?

Thank you!

• Can you say more about the nature of your response variable & how it varies between 0 & 1? Eg, is it a continuous proportion? Nov 17 '15 at 13:21
• It seems you have accidentally created a second account - see our help page on how to merge them. This will make it easier for you to edit your question. Nov 17 '15 at 13:52
• Yes, it is a continuous proportion. I edited the question. Nov 17 '15 at 14:41
• Would it be appropriate to think of this as a classification problem?
– mef
Nov 17 '15 at 14:56
• mef - I'm not sure I understand what you mean by a classification problem. I am not interested in classifying individual subjects to the two subpopulations. I'm trying to compare the degree of bimodality between two bimodally distributed groups. If I did not understand you correctly, please correct me. Nov 17 '15 at 15:01