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Inspired by the recent incident in which a professor was able to [detect that students in his class were cheating][1], I'm curious if there is a standard way to detect if a distribution is bimodal, or a standard measure of the 'bimodality' of a distribution.

Does such a test exist? What are caveats that I should be aware of in such a test?

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You want goodness of fit tests. You can start reading on Wikipedia. – Raphael Jan 3 '11 at 22:27
Here's a link: – leecbaker Jan 3 '11 at 23:14
Just so you know, the link to the cheating incident isn't working. – Mike Spivey Jan 4 '11 at 3:39
up vote 1 down vote accepted

Well the most simple way is to plot the kernel density function. If your data has a bimodal distribution then it will certainly show up in the graph. For more complicated analysis you can try to fit a mixture model, in order to determine the cause of bimodality.

Try asking in site Cross Validated for more answers.

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If you have mathematica, you can use smoothhistogram to quickly get a sense of the modality of your data. This function does what mpiktas suggests. Also, depending on the range of data that you are expecting, you can use the first three central moments of your data to get an idea of its shape.

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It would be interesting to see your idea of using moments to characterize bimodality filled out in greater detail. – hardmath Jan 8 '14 at 19:33

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