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Permalink: http://hdl.handle.net/1866/11052

Size invariant measures of association: characterization and difficulties

Article [Version of Record]
Thumbnail
2014-06-cahier.pdf (206.3Kb)
Is part of
Cahier de recherche ; no. 2014-06.
Publisher(s)
Université de Montréal. Département de sciences économiques.
2014-08
Author(s)
Negri, Margherita
Sprumont, Yves
Affiliation
  • Université de Montréal. Faculté des arts et des sciences. Département de sciences économiques
Abstract(s)
A measure of association is row-size invariant if it is unaffected by the multiplication of all entries in a row of a cross-classification table by a same positive number. It is class-size invariant if it is unaffected by the multiplication of all entries in a class (i.e., a row or a column). We prove that every class-size invariant measure of association as-signs to each m x n cross-classification table a number which depends only on the cross-product ratios of its 2 x 2 subtables. We propose a monotonicity axiom requiring that the degree of association should increase after shifting mass from cells of a table where this mass is below its expected value to cells where it is above .provided that total mass in each class remains constant. We prove that no continuous row-size invariant measure of association is monotonic if m ≥ 4. Keywords: association, contingency tables, margin-free measures, size invariance, monotonicity, transfer principle.
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  • Faculté des arts et des sciences – Département de sciences économiques - Travaux et publications [552]

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