Abstract
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.
Highlights
Test name Identical distribution Embedding approach ANOVA Kuiper two sample test Large-sample Mardia-WatsonWheeler test Log-likelihood ratio ANOVA MANOVA approach Non equal concentration parameters approach ANOVA Watson–Wheeler test Watson’s U2 test Identical mean/median Fisher’s nonparametric test P-test
We focus only on these tests in our explorations of statistical power
When comparing a unimodal and an axial bimodal distribution, which increased in concentration, we found that the MANOVA approach again offered the best power in particular at low samples sizes, followed by the Watson’s U 2 test, the Large-sample Mardia– Watson–Wheeler test and Watson–Wheeler test (Fig. 5)
Summary
Test name Identical distribution Embedding approach ANOVA Kuiper two sample test Large-sample Mardia-WatsonWheeler test Log-likelihood ratio ANOVA MANOVA approach Non equal concentration parameters approach ANOVA Watson–Wheeler test Watson’s U2 test Identical mean/median Fisher’s nonparametric test P-test. Type (1) tests should be sensitive to differences in mean/median as well as to differences in the concentration, . Type (2) tests should be sensitive to differences in the mean/median, but not show differences when only the concentration varies. The most common prerequisite is that distributions should be oriented unimodally (see for example the Watson–Williams test) or that the sample size should exceed a minimum size (e.g. this is true for the Watson’s large-sample nonparametric test)[4]. It is unclear how robust the tests are against violation of the assumptions, but our study will offer guidance on this
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
