P.Mean:  Testing for bimodality (created 2005-05-03, updated 2010-07-06).

This is an update and revision of age on my old site that has some broken links: www.childrensmercy.org/stats/weblog2005/Bimodality.asp.

I have talked about this topic before and it is a rather tricky thing. A recent discussion of tests of bimodality on edstat-l, though, yielded a few promising leads relating to the Dip test of

• J. A. Hartigan, P. M. Hartigan. The Dip Test of Unimodality. The Annals of Statistics. 1985;13(1):70-84. Abstract: "The dip test measures multimodality in a sample by the maximum difference, over all sample points, between the empirical distribution function, and the unimodal distribution function that minimizes that maximum difference. The uniform distribution is the asymptotically least favorable unimodal distribution, and the distribution of the test statistic is determined asymptotically and empirically when sampling from the uniform." [Accessed July 6, 2010]. Available at: http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aos/1176346577.
• P. M. Hartigan. Algorithm AS 217: Computation of the Dip Statistic to Test for Unimodality. Journal of the Royal Statistical Society. Series C (Applied Statistics). 1985;34(3):320-325. [Accessed July 6, 2010]. Available at: http://www.jstor.org/stable/2347485.

Some links to software to run the Dip test are shown below.

• http://cran.r-project.org/web/packages/diptest/diptest.pdf (R)
• http://ideas.repec.org/c/boc/bocode/s456998.html (Stata)
• http://lib.stat.cmu.edu/apstat/217 (FORTRAN)

This work is licensed under a Creative Commons Attribution 3.0 United States License. It was written by Steve Simon and was last modified on 07/06/2010. Category: Statistical theory