Hartigan's Dip Test for Bi-Modality: Rejecting surprising distributions

#1
Hi, I'm new here. Thanks for providing this forum!

I'm checking some separate sample distributions for bi-modality since most but not all of them appear multi-modal in histograms.

Does anyone know if Hartigan's Dip Test is overly liberal in rejecting the null of unimodality? I'm finding that all of my distribution samples have p<0.04 when at least a few of them look pretty unimodal in the histogram (platykurtic and/or skewed, but unimodal). My sample sizes run from 1500 to 190000.

Kolmogorv-Smirnov tests also reject normality and other standard shapes, but this is pretty limiting.

I'm using R to run my analysis with the library(Diptest) and the command dip.test(mydata), which retrieves p values from dip test scores via the lookup table provided with the object qDiptab.

If the conclusion is that none of them are unimodal, then I'd like to have results on how strong the multiple modes are. Any suggestions (the simpler the test the better)?

Please let me know if I should elaborate or clarify anything, or post in the R sub-forum instead.

Thank you for your attention and consideration,
kerrio
 
#2
Hello kerrio,

since you have large sample sizes, it is not surprising that all those distribution tests became significant. I have the same problem with the normality tests. The answer is quite simple, the power increases with sample size and that means that even practically minor deviations from expected values will become significant...unfortunately all I can tell you (but maybe there are other ideas from other forum mebers) is that at least in the case of normality distributions, standard analysis like ANOVA or regressions are relatively robust against violations of the normality assumption if you have a large sample size. If this is the same case with those bimodality test I would just ignore it and proceed with my main analysis whereby mentioning your significant deviations in your study publication paper...but since I'm not experienced with the Dip Test I cannot tell you anything about it :/...
hope I could help you a little bit anyways ;)

Greetings,
Marina