Upsilon
Another Test of Association for Count Data
Description
The Upsilon test assesses association among categorical variables against the null hypothesis of independence (Luo 2021 MS thesis; ProQuest Publication No. 28649813). While promoting dominant function patterns, it demotes non-dominant function patterns. It is robust to low expected count---continuity correction like Yates's seems unnecessary. Using a common null population following a uniform distribution, contingency tables are comparable by statistical significance---not the case for most association tests defining a varying null population by tensor product of observed marginals. Although Pearson's chi-squared test, Fisher's exact test, and Woolf's G-test (related to mutual information) are useful in some contexts, the Upsilon test appeals to ranking association patterns not necessarily following same marginal distributions, such as in count data from DNA and RNA sequencing---a rapidly expanding frontier in modern science.
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