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dc.contributor.authorRuxton, Graeme D.
dc.contributor.authorMalkemper, E. Pascal
dc.contributor.authorLandler, Lukas
dc.identifier.citationRuxton , G D , Malkemper , E P & Landler , L 2023 , ' Evaluating the power of a recent method for comparing two circular distributions : an alternative to the Watson U 2 test ' , Scientific Reports , vol. 13 .
dc.identifier.otherPURE: 290843464
dc.identifier.otherPURE UUID: 1175929d-b3e4-441f-a57d-f98ce462e656
dc.identifier.otherJisc: 1156667
dc.identifier.otherpublisher-id: s41598-023-36960-1
dc.identifier.othermanuscript: 36960
dc.identifier.otherScopus: 85162889396
dc.identifier.otherORCID: /0000-0001-8943-6609/work/139156732
dc.descriptionFunding: This research was funded in whole, or in part, by the Austrian Science Fund (FWF) Grant Number: P32586 to LL. EPM receives funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 948728).en
dc.description.abstractSome data are collected on circular (rather than linear) scales. Often researchers are interested in comparing two samples of such circular data to test the hypothesis that they came from the same underlying population. Recently, we compared 18 statistical approaches to testing such a hypothesis, and recommended two as particularly effective. A very recent publication introduced a novel statistical approach that was claimed to outperform the methods that we had indicated were highest performing. However, the evidence base for this claim was limited. Here we perform simulation studies to offer a more detailed comparison of the new “Angular Randomisation Test” (ART) with existing tests. We expand previous evaluations in two ways: exploring small and medium sized samples, and exploring a range of different shapes for the underlying distribution(s). We find that the ART controls type I error rates at the nominal level. The ART had greater power than established methods in detecting a difference in underlying distribution caused by a shift around the circle. Its performance advantage in this case was strongest when samples where small and unbalanced in size. When the difference between underlying unimodal distributions was in shape rather than central tendency, then the ART was at least as good (and sometimes considerably more powerful) than the established methods, except when distributions samples were small and uneven in size, and the smaller sample came from a more concentrated underlying distribution. In such cases its power could be markedly inferior to established alternatives. The ART was also inferior to alternatives in dealing with axially distributed data. We conclude that under widely-encountered circumstances the ART test can be recommended for its simplicity of implementation, but researchers should be aware of situations where it cannot be recommended.
dc.relation.ispartofScientific Reportsen
dc.rightsCopyright © The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
dc.subjectQL Zoologyen
dc.subjectHA Statisticsen
dc.titleEvaluating the power of a recent method for comparing two circular distributions : an alternative to the Watson U2 testen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. School of Biologyen
dc.contributor.institutionUniversity of St Andrews. Centre for Biological Diversityen
dc.contributor.institutionUniversity of St Andrews. Institute of Behavioural and Neural Sciencesen
dc.description.statusPeer revieweden

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