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Asymmetry is an inherent property of bivariate associations and thereforemust not be ignored. The currently applicable dependence measures mask thepotential asymmetry of the underlying dependence structure by implicitlyassuming that quantity Y is equally dependent on quantity X, and vice versa,which is generally not true. We introduce the copula-based dependence measureqad that quantifies asymmetry. Specifically, qad is applicable in generalsituations, is sensitive to noise in data, detects asymmetry in dependence andreliably quantifies the information gain/predictability of quantity Y givenknowledge of quantity X, and vice versa. Using real-world data sets, wedemonstrate the relevance of asymmetry in associations. Asymmetry in dependenceis a novel category of information that provides substantial information gainin analyses of bivariate associations.

A copula-based measure for quantifying asymmetry in dependence and associations