Size invariant measures of association: characterization and difficulties

Margherita Negri and Yves Sprumont ()

Cahiers de recherche from Universite de Montreal, Departement de sciences economiques

Abstract: 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.

Pages: 26 pages
Date: 2014
New Economics Papers: this item is included in nep-gth
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http://hdl.handle.net/1866/11052 (application/pdf)

Related works:
Journal Article: Size invariant measures of association: Characterization and difficulties (2015)
Working Paper: Size Invariant Measures of Association: Characterization and Difficulties (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:mtl:montde:2014-06

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