Measures of association play a role in selecting 2×2 tables exhibiting strong dependence in high-dimensionalbinary data. Several measures are in use differing on specific tables and in their dependence on the margins.We study a 2-dimensional group of margin transformations on the 3-dimensional manifold of all2×2 probability tables. The margin transformations allow introducing natural coordinates that identify with the real 3-space such that the x-axis corresponds to and margins vary onplanes x =const. We use these coordinates to visualise and compare measures of association with respectto their dependence on the margins given the odds-ratio, their limit behaviour when cells approach zeroand their weighting properties. We propose a novel measure of association in which tables with singlesmall entries are up-weighted but those with skewed margins are down-weighted according to the relativeentropy among the tables of the same odds-ratio.
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