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 m
ay 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 Liebschers 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.
Problems in econometrics, insurance, reliability engineering, and statistics quite often rely on the assumption that certain functions are non-decreasing. To satisfy this requirement, researchers frequently model the underlying phenomena using parame
tric and semi-parametric families of functions, thus effectively specifying the required shapes of the functions. To tackle these problems in a non-parametric way, in this paper we suggest indices for measuring the lack of monotonicity in functions. We investigate properties of the indices and also offer a convenient computational technique for practical use.
