Advice on comparing two independent samples of circular data in biology

Lukas Landler*, Graeme D. Ruxton, E. Pascal Malkemper

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


Many biological variables are recorded on a circular scale and therefore need different statistical treatment. A common question that is asked of such circular data involves comparison between two groups: Are the populations from which the two samples are drawn differently distributed around the circle? We compared 18 tests for such situations (by simulation) in terms of both abilities to control Type-I error rate near the nominal value, and statistical power. We found that only eight tests offered good control of Type-I error in all our simulated situations. Of these eight, we were able to identify the Watson’s U2 test and a MANOVA approach, based on trigonometric functions of the data, as offering the best power in the overwhelming majority of our test circumstances. There was often little to choose between these tests in terms of power, and no situation where either of the remaining six tests offered substantially better power than either of these. Hence, we recommend the routine use of either Watson’s U2 test or MANOVA approach when comparing two samples of circular data.
Original languageEnglish
Article number20337
Number of pages10
JournalScientific Reports
Publication statusPublished - 13 Oct 2021


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