USP: an independence test that improves on Pearson's chi-squared and the G-test.
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Publication Date
2021-12Journal Title
Proc Math Phys Eng Sci
ISSN
1364-5021
Publisher
The Royal Society
Language
eng
Type
Article
This Version
VoR
Metadata
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Berrett, T. B., & Samworth, R. J. (2021). USP: an independence test that improves on Pearson's chi-squared and the G-test.. Proc Math Phys Eng Sci https://doi.org/10.1098/rspa.2021.0549
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 χ 2 -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.
Keywords
Independence, Permutation Test, Fisher’s Exact Test, Statistic, G-test, Pearson’s Χ2-test
Sponsorship
Engineering and Physical Sciences Research Council (EP/N031938/1)
Engineering and Physical Sciences Research Council (EP/P031447/1)
European Commission Horizon 2020 (H2020) ERC (101019498)
Identifiers
35153605, PMC8652272
External DOI: https://doi.org/10.1098/rspa.2021.0549
This record's URL: https://www.repository.cam.ac.uk/handle/1810/335205
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