For two-way contingency tables, whose row and column variables have nominal categories, we introduce a new partial order according to the strength of dependence within the class of all contingency tables with given margins. The order holds among tables which share the same configuration of signs in the deviation from independence (contingencies) and takes into account the absolute value of these contingencies. Our order, which seems to possess a more direct and intuitive interpretation relative to similar ones available in the literature, is characterized by a sequence of frequency transfers over a closed path, which involve an even number of cells and leave the marginal distributions unchanged. We derive necessary and sufficient conditions for maximal (minimal) tables, according to our notion of dependence. Furthermore a simple algorithm is provided to check these conditions. Finally, an associated measure of dependence is briefly mentioned.

Greselin, F., Zenga, M. (2004). A partial ordering of dependence for contingency tables. STATISTICA & APPLICAZIONI, 2(1), 53-71.

A partial ordering of dependence for contingency tables

GRESELIN, FRANCESCA;ZENGA, MICHELE
2004

Abstract

For two-way contingency tables, whose row and column variables have nominal categories, we introduce a new partial order according to the strength of dependence within the class of all contingency tables with given margins. The order holds among tables which share the same configuration of signs in the deviation from independence (contingencies) and takes into account the absolute value of these contingencies. Our order, which seems to possess a more direct and intuitive interpretation relative to similar ones available in the literature, is characterized by a sequence of frequency transfers over a closed path, which involve an even number of cells and leave the marginal distributions unchanged. We derive necessary and sufficient conditions for maximal (minimal) tables, according to our notion of dependence. Furthermore a simple algorithm is provided to check these conditions. Finally, an associated measure of dependence is briefly mentioned.
Articolo in rivista - Articolo scientifico
Scientifica
Dependence ordering, stochastic ordering, contingency tables, measures of dependence, bivariate distributions with given margins
English
53
71
19
Greselin, F., Zenga, M. (2004). A partial ordering of dependence for contingency tables. STATISTICA & APPLICAZIONI, 2(1), 53-71.
Greselin, F; Zenga, M
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/4644
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