dc.contributor.author Berrett, Thomas B en dc.contributor.author Samworth, Richard en dc.date.accessioned 2021-11-13T00:30:34Z dc.date.available 2021-11-13T00:30:34Z dc.identifier.issn 1364-5021 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/330630 dc.description.abstract We 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.publisher The Royal Society dc.rights All rights reserved dc.rights.uri http://www.rioxx.net/licenses/all-rights-reserved dc.subject stat.ME en dc.subject stat.ME en dc.subject math.ST en dc.subject stat.AP en dc.subject stat.ML en dc.subject stat.TH en dc.subject 62H17, 62H20, 62F03, 62F05, 62E20 en dc.title USP: an independence test that improves on Pearson's chi-squared and the $G$-test en dc.type Article dc.identifier.doi 10.17863/CAM.78074 dcterms.dateAccepted 2021-11-10 en rioxxterms.version AM rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved en rioxxterms.licenseref.startdate 2021-11-10 en dc.contributor.orcid Samworth, Richard [0000-0003-2426-4679] rioxxterms.type Journal Article/Review en pubs.funder-project-id LANCASTER UNIVERSITY (FB EPSRC) (EP/N031938/1) pubs.funder-project-id EPSRC (EP/P031447/1) pubs.funder-project-id European Commission Horizon 2020 (H2020) ERC (101019498) cam.orpheus.counter 17 * rioxxterms.freetoread.startdate 2024-11-12
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