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Here are some distributions of US political views by industry:

enter image description here

After observing their mostly bimodal nature, I would like to measure the degree of bimodality in each of the distributions for the purpose of comparison with the same distribution over time, as well as for comparison between distributions (between industries in this case).

Presuming I first test for bimodality using some established methods, what should my next steps be to determine the extent of the bimodality?

stevec
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    "Extent of bimodality" isn't well-defined, so it'd be helpful to know what you're shooting for. Most of those plots are indeed bimodal, but one could perhaps argue that Lawyers are less bimodal since there's a lot in between the modes, or that Academics are less bimodal because they are so skewed. Your preferred metric will depend on what exactly you're trying to measure. Which among these plots would you consider the most or least bimodal? – Nuclear Hoagie Jan 12 '21 at 15:13
  • Great questions. I'm hoping some measures have already been developed. But if I had to guess, I would say three things that could form part of the measurement are i) the proportion of the distribution that is on the distribution's fringes, ii) the extent of the difference between the peaks and trough of the distribution, iii) the proportionality between the two modes (note how some are very U shaped, whereas others are lop sided). But I hope there are already established methods that take into account these (and any other relevant) considerations. – stevec Jan 12 '21 at 15:35
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    Have a look at [this review paper](https://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article=1120&context=jmasm) – kjetil b halvorsen Jan 13 '21 at 01:53
  • @kjetilbhalvorsen thanks I'll check it out – stevec Jan 13 '21 at 02:21

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