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

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 co-monotonicity (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.