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Compositional data and Simpson’s paradox

Simpson’s paradox, also known as amalgamation or aggregation paradox, appears when dealing with proportions. Proportions are by construction parts of a whole, which can be interpreted as compositions assuming they only carry relative information. The Aitchison inner product space structure of the simplex, the sample space of compositions, explains the appearance of the paradox, given that amalgamation is a nonlinear operation within that structure. Here we propose to use balances, which are specific elements of this structure, to analyse situations where the paradox might appear. With the proposed approach we obtain that the centre of the tables analysed is a natural way to compare them, which avoids by construction the possibility of a paradox. Key words: Aitchison geometry, geometric mean, orthogonal projection

Geologische Vereinigung; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Càtedra Lluís Santaló d’Aplicacions de la Matemàtica; Generalitat de Catalunya, Departament d’Innovació, Universitats i Recerca; Ministerio de Educación y Ciencia; Ingenio 2010.

Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada

Manager: Daunis i Estadella, Josep
Martín Fernández, Josep Antoni
Other contributions: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Author: Egozcue, Juan José
Pawlowsky-Glahn, Vera
Date: 2008 May 28
Abstract: Simpson’s paradox, also known as amalgamation or aggregation paradox, appears when dealing with proportions. Proportions are by construction parts of a whole, which can be interpreted as compositions assuming they only carry relative information. The Aitchison inner product space structure of the simplex, the sample space of compositions, explains the appearance of the paradox, given that amalgamation is a nonlinear operation within that structure. Here we propose to use balances, which are specific elements of this structure, to analyse situations where the paradox might appear. With the proposed approach we obtain that the centre of the tables analysed is a natural way to compare them, which avoids by construction the possibility of a paradox. Key words: Aitchison geometry, geometric mean, orthogonal projection
Geologische Vereinigung; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Càtedra Lluís Santaló d’Aplicacions de la Matemàtica; Generalitat de Catalunya, Departament d’Innovació, Universitats i Recerca; Ministerio de Educación y Ciencia; Ingenio 2010.
Format: application/pdf
Citation: Egozcue, J.J.; Pawlowsky Glahn, V. ’Compositional data and Simpson’s paradox’ a CODAWORK’08. Girona: La Universitat, 2008 [consulta: 12 maig 2008]. Necessita Adobe Acrobat. Disponible a Internet a: http://hdl.handle.net/10256/718
Document access: http://hdl.handle.net/10256/718
Language: eng
Publisher: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Rights: Tots els drets reservats
Subject: Geometria d’Aitchison
Variables (Estadística)
Title: Compositional data and Simpson’s paradox
Type: info:eu-repo/semantics/conferenceObject
Repository: DUGiDocs

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