Size Invariant Measures of Association: Characterization and Difficulties

Margherita Negri and Yves Sprumont ()

Cahiers de recherche from Centre interuniversitaire de recherche en économie quantitative, CIREQ

Abstract: A measure of association is row-size invariant if it is unaffected by the mutliplication of all entries in a row of a cross-classi cation table by a same positive number. It is class-size invariant if it is unaffected by the mutliplication 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 mxn cross-classi fication table a number which depends only on the cross-product ratios of its 2x2 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 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2014
New Economics Papers: this item is included in nep-gth
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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:montec:10-2014

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