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Three-way association measure decompositions: The Delta index
Authors:Rosaria Lombardo
Institution:Department of Management, Accounting and Quantitative Methods, Economics Faculty, Second University of Naples, via Gran Priorato di Malta, 81043 Capua (CE), Italy
Abstract:In this paper we describe a general framework to decompose three-way association measures for contingency tables, in particular symmetric and non-symmetric measures will be discussed, like Pearson's index, Marcotorchino's index, whose special case is the Gray–Williams index, and a new non-symmetric one will be proposed, called the Delta index. After showing the orthogonal decomposition of these indices, practical examples illustrating the different decompositions will be given.
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