  We present a framework for selecting and developing measures of dependence
when the goal is the quantification of a relationship between two variables,
not simply the establishment of its existence. Much of the literature on
dependence measures is focused, at least implicitly, on detection or revolves
around the inclusion/exclusion of particular axioms and discussing which
measures satisfy said axioms. In contrast, we start with only a few
nonrestrictive guidelines focused on existence, range and interpretability,
which provide a very open and flexible framework. For quantification, the most
crucial is the notion of interpretability, whose foundation can be found in the
work of Goodman and Kruskal [Measures of Association for Cross Classifications
(1979) Springer], and whose importance can be seen in the popularity of tools
such as the $R^2$ in linear regression. While Goodman and Kruskal focused on
probabilistic interpretations for their measures, we demonstrate how more
general measures of information can be used to achieve the same goal. To that
end, we present a strategy for building dependence measures that is designed to
allow practitioners to tailor measures to their needs. We demonstrate how many
well-known measures fit in with our framework and conclude the paper by
presenting two real data examples. Our first example explores U.S. income and
education where we demonstrate how this methodology can help guide the
selection and development of a dependence measure. Our second example examines
measures of dependence for functional data, and illustrates them using data on
geomagnetic storms.
