Size invariant measures of association: characterization and difficulties

Margherita Negri, Yves Sprumont

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

    Keywords

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

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