Analysis Of Several Categorical Data Using Measure of Proportional Reduction In Variation

Kouji Yamamoto; Kouji Tahata; Nobuko Miyamoto; Sadao Tomizawa

doi:10.1142/9789814343763_0026

Analysis Of Several Categorical Data Using Measure of Proportional Reduction In Variation

Kouji Yamamoto, Kouji Tahata, Nobuko Miyamoto, Sadao Tomizawa

Department of Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

For a two-way contingency table with nominal row and column variables, the measures which describe the proportional reduction in variation (PRV) from the marginal distribution of one variable to the conditional distribution given the other variable are proposed by Goodman and Kruskal (1954), Theil (1970), and Freeman (1987, p. 101). Tomizawa, Seo and Ebi (1997), and Miyamoto, Usui and Tomizawa (2005) proposed the generalization of those measures. Tomizawa, Miyamoto and Yajima (2002), and Yamamoto and Tomizawa (2009) proposed the PRV measures for a nominal-ordinal contingency table and for an ordinal-ordinal contingency table, respectively. The present paper (1) reviews these PRY measures and (2) analyzes and compares between several categorical data using these PRY measures.

Original language	English
Title of host publication	Quantum Bio-informatics IV
Subtitle of host publication	From Quantum Information to Bio-informatics
Publisher	World Scientific Publishing Co.
Pages	339-354
Number of pages	16
ISBN (Electronic)	9789814343763
ISBN (Print)	9789814343756
DOIs	https://doi.org/10.1142/9789814343763_0026
Publication status	Published - 1 Jan 2011

Keywords

Concentration coefficient
Measure
Proportional reduction in variation
Square contingency table
Total uncertainty coefficient

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10.1142/9789814343763_0026

Cite this

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abstract = "For a two-way contingency table with nominal row and column variables, the measures which describe the proportional reduction in variation (PRV) from the marginal distribution of one variable to the conditional distribution given the other variable are proposed by Goodman and Kruskal (1954), Theil (1970), and Freeman (1987, p. 101). Tomizawa, Seo and Ebi (1997), and Miyamoto, Usui and Tomizawa (2005) proposed the generalization of those measures. Tomizawa, Miyamoto and Yajima (2002), and Yamamoto and Tomizawa (2009) proposed the PRV measures for a nominal-ordinal contingency table and for an ordinal-ordinal contingency table, respectively. The present paper (1) reviews these PRY measures and (2) analyzes and compares between several categorical data using these PRY measures.",

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Analysis Of Several Categorical Data Using Measure of Proportional Reduction In Variation

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Keywords

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