On Association Measures for Continuous Variables and Correction for Chance

Abstract

This paper studies correction for chance for association measures for continuous variables. The set of linear transformations of Pearson’s product-moment correlation is used as the domain of the correction for chance function. Examples of measures in this set are Tucker’s congruence coefficient, Jobson’s coefficient, and Pearson’s correlation. An equivalence relation on the set of linear transformations is defined. The fixed points of the correction for chance function are characterized. It is shown that each linear transformation is mapped to the fixed point in its equivalence class.