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Measures of association play a role in selecting 2x2 tables exhibiting strongdependence in high-dimensional binary data. Several measures are in usediffering on specific tables and in their dependence on the margins.  We study a 2-dimensional group of margin transformations on the 3-dimensionalmanifold T of all 2x2 probability tables. The margin transformations allowintroducing natural coordinates that identify T with the real 3-space such thatthe x-axis corresponds to log(sqrt(odds-ratio)) and margins vary on planesx=const. We use these coordinates to visualise and compare measures ofassociation with respect to their dependence on the margins given theodds-ratio, their limit behaviour when cells approach zero and their weightingproperties.  We propose a novel measure of association in which tables with single smallentries are up-weighted but those with skewed margins are down-weightedaccording to the relative entropy among the tables of the same odds-ratio.

Comparing measures of association in 2x2 probability tables