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Size invariant measures of association: characterization and difficulties

Research output: Contribution to journalArticle

Author(s)

Margherita Negri, Yves Sprumont

School/Research organisations

Abstract

A measure of association on cross-classification tables is row-size invariant if it is unaffected by the multiplication of all entries in a row by the 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 assigns to each cross-classification table a number which depends only on the cross-product ratios of its 2×2 subtables. We submit that the degree of association should increase when mass is shifted from cells containing a proportion of observations lower than what is expected under statistical independence to cells containing a proportion higher than expected–provided that total mass in each class remains unchanged. We prove that no continuous row-size invariant measure of association satisfies this monotonicity axiom if there are at least four rows.
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Details

Original languageEnglish
Pages (from-to)115-122
Number of pages8
JournalMathematical Social Sciences
Volume75
Early online date20 Mar 2015
DOIs
Publication statusPublished - May 2015

    Research areas

  • Association, Contingency tables, Margin-free measures, Size invariance, Monotonicity, Transfer principle

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