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

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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 paperwe explore a novel approach based on a LOCindex,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.
Opis fizyczny
  • Department of Mathematics, Universitas Gadjah Mada, Yogyakarta 55281, Indonesia; and Department
    of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario N6A 5B7, Canada
  • Department of Statistical and Actuarial Sciences, University of Western Ontario,
    London, Ontario N6A 5B7, Canada
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