USP: an independence test that improves on Pearson’s chi-squared and the G-test

We present the [Formula: see text]-statistic permutation (USP) test of independence in the context of discrete data displayed in a contingency table. Either Pearson’s [Formula: see text]-test of independence, or the [Formula: see text]-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 [Formula: see text]-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 [Formula: see text]-test and Fisher’s exact test, and on real data. The USP test is implemented in the R package USP.