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Size invariant measures of association: Characterization and difficulties

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  • Negri, Margherita
  • Sprumont, Yves

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.

Suggested Citation

  • Negri, Margherita & Sprumont, Yves, 2015. "Size invariant measures of association: Characterization and difficulties," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 115-122.
    • Handle: RePEc:eee:matsoc:v:75:y:2015:i:c:p:115-122
    DOI: 10.1016/j.mathsocsci.2015.03.002
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