Predictive Measures of Ordinal Association

For selecting and interpreting appropriate measures of association, a "proportional-reduction-in-error" (P-R-E) criterion is useful. However, efforts to give a P-R-E interpretation to measures of ordinal association have not been successful, especially in delineating the "form" or "shape" of ordinal association. An effort is therefore made in this paper to introduce the notion of relevant forms of ordinal association, such as strict monotonic, monotonic, and nonmonotonic associations, and to suggest a few P-R-E measures that would assess such particular forms of association in ordinal data.