1 Institute for Medical Informatics, Statistics and Epidemiology, Leipzig, Germany
2 LIFE Research Center University of Leipzig, Leipzig, Germany
Measures of association play a role in selecting 2×2 tables exhibiting strong dependence in high-dimensional
binary 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
2×2 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 on
planes x =const. We use these coordinates to visualise and compare measures of association with respect
to their dependence on the margins given the odds-ratio, their limit behaviour when cells approach zero
and their weighting properties. We propose a novel measure of association in which tables with single
small entries are up-weighted but those with skewed margins are down-weighted according to the relative
entropy among the tables of the same odds-ratio.
Keywords: Entropy, Margin, Measures of association, Odds-ratio, Statistical dependence, Two by two probability tables.
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