Measuring association via lack of co-monotonicity: The LOC index and a problem of educational assessment

Abstract

Measuring association, or the lack of it, between variables plays an important role in a variety of research areas, including education, which is of our primary interest in this paper. Given, for example, student marks on several study subjects, we may for a number of reasons be interested in measuring the lack of comonotonicity (LOC) between the marks, which rarely follow monotone, let alone linear, patterns. For this purpose, in this paper we explore a novel approach based on a LOC index,which is related to, yet substantially different from, Eckhard Liebscher's recently suggested coefficient of monotonically increasing dependence. To illustrate the new technique, we analyze a data-set of student marks on mathematics, reading and spelling.