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dc.contributor.authorBerrett, Thomas Ben
dc.contributor.authorSamworth, Richarden
dc.date.accessioned2021-11-13T00:30:34Z
dc.date.available2021-11-13T00:30:34Z
dc.identifier.issn1364-5021
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/330630
dc.description.abstractWe present the U-Statistic Permutation (USP) test of independence in the context of discrete data displayed in a contingency table. Either Pearson's chi-squared test of independence, or the G-test, are typically used for this task, but we argue that these tests have serious deficiencies, both in terms of their inability to control the size of the test, and their power properties. By contrast, the USP test is guaranteed to control the size of the test at the nominal level for all sample sizes, has no issues with small (or zero) cell counts, and is able to detect distributions that violate independence in only a minimal way. The test statistic is derived from a U-statistic estimator of a natural population measure of dependence, and we prove that this is the unique minimum variance unbiased estimator of this population quantity. The practical utility of the USP test is demonstrated on both simulated data, where its power can be dramatically greater than those of Pearson's test, the G-test and Fisher's exact test, and on real data. The USP test is implemented in the R package USP.
dc.publisherThe Royal Society
dc.rightsAll rights reserved
dc.rights.urihttp://www.rioxx.net/licenses/all-rights-reserved
dc.subjectstat.MEen
dc.subjectstat.MEen
dc.subjectmath.STen
dc.subjectstat.APen
dc.subjectstat.MLen
dc.subjectstat.THen
dc.subject62H17, 62H20, 62F03, 62F05, 62E20en
dc.titleUSP: an independence test that improves on Pearson's chi-squared and the $G$-testen
dc.typeArticle
dc.identifier.doi10.17863/CAM.78074
dcterms.dateAccepted2021-11-10en
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2021-11-10en
dc.contributor.orcidSamworth, Richard [0000-0003-2426-4679]
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idLANCASTER UNIVERSITY (FB EPSRC) (EP/N031938/1)
pubs.funder-project-idEPSRC (EP/P031447/1)
pubs.funder-project-idEuropean Commission Horizon 2020 (H2020) ERC (101019498)
cam.orpheus.counter17*
rioxxterms.freetoread.startdate2024-11-12


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