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dc.contributor.authorBerrett, Thomas B.
dc.contributor.authorSamworth, Richard J.
dc.date.accessioned2021-12-24T14:38:17Z
dc.date.available2021-12-24T14:38:17Z
dc.date.issued2021-12-08
dc.date.submitted2021-07-07
dc.identifier.issn1364-5021
dc.identifier.otherrspa20210549
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/331814
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 χ2-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.languageen
dc.publisherThe Royal Society
dc.subjectResearch articles
dc.subjectindependence
dc.subjectPearson’s χ2-test
dc.subjectG-test
dc.subjectpermutation test
dc.subjectstatistic
dc.subjectFisher’s exact test
dc.titleUSP: an independence test that improves on Pearson’s chi-squared and the G -test
dc.typeArticle
dc.date.updated2021-12-24T14:38:16Z
prism.issueIdentifier2256
prism.publicationNameProceedings of the Royal Society A
prism.volume477
dc.identifier.doi10.17863/CAM.79263
dcterms.dateAccepted2021-11-10
rioxxterms.versionofrecord10.1098/rspa.2021.0549
rioxxterms.versionAO
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidSamworth, Richard J. [0000-0003-2426-4679]
dc.identifier.eissn1471-2946
pubs.funder-project-idH2020 European Research Council (101019498)
pubs.funder-project-idEPSRC (EP/N031938/1, EP/P031447/1)


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