Size invariant measures of association : characterization and difficulties
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.
Citation
Negri , M & Sprumont , Y 2015 , ' Size invariant measures of association : characterization and difficulties ' , Mathematical Social Sciences , vol. 75 , pp. 115-122 . https://doi.org/10.1016/j.mathsocsci.2015.03.002
Publication
Mathematical Social Sciences
Status
Peer reviewed
ISSN
0165-4896Type
Journal article
Description
Sprumont acknowledges support from the Fonds de Recherche sur la Soci été et la Culture of Québec.Collections
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