Size invariant measures of association : characterization and difficulties
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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.
Negri , M & Sprumont , Y 2015 , ' Size invariant measures of association : characterization and difficulties ' Mathematical Social Sciences , vol 75 , pp. 115-122 . DOI: 10.1016/j.mathsocsci.2015.03.002
Mathematical Social Sciences
©2015 Elsevier B.V. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://dx.doi.org/10.1016/j.mathsocsci.2015.03.002
Sprumont acknowledges support from the Fonds de Recherche sur la Soci été et la Culture of Québec.