1. USP: an independence test that improves on Pearson's chi-squared and the $G$-test
- Author
-
Berrett, Thomas B, Samworth, Richard, Samworth, Richard J. [0000-0003-2426-4679], Apollo - University of Cambridge Repository, Samworth, Richard [0000-0003-2426-4679], and Samworth, Richard J [0000-0003-2426-4679]
- Subjects
FOS: Computer and information sciences ,statistic ,General Mathematics ,independence ,General Physics and Astronomy ,Mathematics - Statistics Theory ,Machine Learning (stat.ML) ,Statistics Theory (math.ST) ,Fisher���s exact test ,Statistics - Applications ,01 natural sciences ,Fisher’s exact test ,G-test ,Methodology (stat.ME) ,010104 statistics & probability ,Statistics - Machine Learning ,Research articles ,62H17, 62H20, 62F03, 62F05, 62E20 ,0502 economics and business ,FOS: Mathematics ,stat.TH ,Applications (stat.AP) ,0101 mathematics ,stat.AP ,Statistics - Methodology ,050205 econometrics ,Pearson���s ��2-test ,05 social sciences ,General Engineering ,Pearson’s χ 2 -test ,math.ST ,stat.ML ,Pearson’s χ2-test ,stat.ME ,permutation test - 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 and the $G$-test, and on real data. The USP test is implemented in the R package USP., Comment: 27 pages, 7 figures
- Published
- 2021
- Full Text
- View/download PDF