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Size invariant measures of association: characterization and difficulties

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Size invariant measures of association : characterization and difficulties. / Negri, Margherita; Sprumont, Yves.

In: Mathematical Social Sciences, Vol. 75, 05.2015, p. 115-122.

Research output: Contribution to journalArticlepeer-review

Harvard

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

APA

Negri, M., & Sprumont, Y. (2015). Size invariant measures of association: characterization and difficulties. Mathematical Social Sciences, 75, 115-122. https://doi.org/10.1016/j.mathsocsci.2015.03.002

Vancouver

Negri M, Sprumont Y. Size invariant measures of association: characterization and difficulties. Mathematical Social Sciences. 2015 May;75:115-122. https://doi.org/10.1016/j.mathsocsci.2015.03.002

Author

Negri, Margherita ; Sprumont, Yves. / Size invariant measures of association : characterization and difficulties. In: Mathematical Social Sciences. 2015 ; Vol. 75. pp. 115-122.

Bibtex - Download

@article{11341051b0204cf7943191b75fdb3232,
title = "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-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.",
keywords = "Association, Contingency tables, Margin-free measures, Size invariance, Monotonicity, Transfer principle",
author = "Margherita Negri and Yves Sprumont",
note = "Sprumont acknowledges support from the Fonds de Recherche sur la Soci {\'e}t{\'e} et la Culture of Qu{\'e}bec.",
year = "2015",
month = may,
doi = "10.1016/j.mathsocsci.2015.03.002",
language = "English",
volume = "75",
pages = "115--122",
journal = "Mathematical Social Sciences",
issn = "0165-4896",
publisher = "Elsevier",

}

RIS (suitable for import to EndNote) - Download

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 -

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