TY - JOUR

T1 - Size invariant measures of association

T2 - characterization and difficulties

AU - Negri, Margherita

AU - Sprumont, Yves

N1 - Sprumont acknowledges support from the Fonds de Recherche sur la Soci été et la Culture of Québec.

PY - 2015/5

Y1 - 2015/5

N2 - 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-sizeinvariant 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.

AB - 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-sizeinvariant 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.

KW - Association

KW - Contingency tables

KW - Margin-free measures

KW - Size invariance

KW - Monotonicity

KW - Transfer principle

U2 - 10.1016/j.mathsocsci.2015.03.002

DO - 10.1016/j.mathsocsci.2015.03.002

M3 - Article

VL - 75

SP - 115

EP - 122

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

SN - 0165-4896

ER -