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Decompositions of models and measures for statistical analysis ofcontingency tables

Research Project

Project/Area Number 20540136
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionTokyo University of Science

Principal Investigator

TOMIZAWA Sadao  Tokyo University of Science, 理工学部, 教授 (50188778)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords対称性 / モデル / 尺度 / 正方分割表 / 統計数学
Research Abstract

For example, a set of people can be divided into 16 cells by right and left eye visions with 4 categories, called 4x4 square contingency tables. The probability that an observation will fall into a given cell is unknown. For eye vision, we are interested in the structure of symmetry and asymmetry, and the degree of asymmetry. This research had proposed some new model of symmetry and asymmetry, and measures, and their decompositions.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (47 results)

All 2011 2010 2009 2008 Other

All Journal Article (21 results) (of which Peer Reviewed: 21 results) Presentation (22 results) Remarks (4 results)

  • [Journal Article] Linear ordinal quasi-symmetry model and decomposition of symmetry for multi-way tables.2011

    • Author(s)
      Tahata, K., Yamamoto, H., Tomizawa, S.
    • Journal Title

      Mathematical Methods of Statistics (to appear.)

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Measure of departure from marginal homogeneity using marginal odds for multi-way tables with ordered categories.2011

    • Author(s)
      Iki K., Tahata K., Tomizawa S.
    • Journal Title

      Journal of Applied Statistics (to appear.)

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Measure of uniform association based on concordant and discordant pairs for cross-classifications.2011

    • Author(s)
      Tahata K., Tomizawa S.
    • Journal Title

      Journal of Statistical Theory and Practice (to appear.)

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On partitioning conditional independence model for three-way contingency tables.2011

    • Author(s)
      Iki K., Tahata K., Tomizawa S.
    • Journal Title

      Model Assisted Statistics and Applications : An International Journal (to appear.)

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Decomposing asymmetry into extended quasi-symmetry and marginal homogeneity for cumulative probabilities in square contingency tables.2011

    • Author(s)
      Yamamoto K., Ando S., Tomizawa S.
    • Journal Title

      Journal of Statistics : Advances in Theory and Applications (to appear.)

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Double linear diagonals-parameter symmetry and decomposition of double symmetry for square tables.2010

    • Author(s)
      Tahata K., Tomizawa S.
    • Journal Title

      Statistical Methods and Applications : Journal of the Italian Statistical Society Vol.19

      Pages: 307-318

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Measure of departure from average cumulative symmetry for square contingency tables with ordered categories.2010

    • Author(s)
      Tahata K., Miyazawa K. Tomizawa S.
    • Journal Title

      American Journal of Biostatistics Vol.1

      Pages: 62-66

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Measures of proportional reduction in error for two-way contingency tables with nominal categories.2010

    • Author(s)
      Yamamoto K., Tomizawa S.
    • Journal Title

      Biostatistics, Bioinformatics and Biomathematics Vol.2

      Pages: 43-52

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Double linear diagonals-parameter symmetry and decomposition of double symmetry for square tables2010

    • Author(s)
      Tahata, K., Tomizawa, S.
    • Journal Title

      Statistical Methods and Applications : Journal of the Italian Statistical Society

      Volume: 19 Pages: 307-318

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Measures of proportional reduction in error for two-way contingency tables with nominal categories2010

    • Author(s)
      Yamamoto, K., Tomizawa, S.
    • Journal Title

      Biostatistics, Bioinformatics and Biomathematics

      Volume: 2 Pages: 43-52

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Measure of departure from average cumulative symmetry for square contingency tables with ordered categories2010

    • Author(s)
      Tahata, K., Miyazawa, K., Tomizawa, S.
    • Journal Title

      American Journal of Biostatistics

      Volume: 1 Pages: 62-66

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A measure of departure from average symmetry for square contingency tables with ordered categories.2009

    • Author(s)
      Tahata K., Yamamoto K., Nagatani N., Tomizawa S.
    • Journal Title

      Austrian Journal of Statistics Vo.38

      Pages: 101-108

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Ridit score type quasi-symmetry and decomposition of symmetry for square contingency tables with ordered categories.2009

    • Author(s)
      Iki K., Tahata K., Tomizawa S.
    • Journal Title

      Austrian Journal of Statistics Vol.38

      Pages: 183-192

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Decomposition of symmetry using two-ratios-parameter symmetry model and orthogonality for square contingency tables2009

    • Author(s)
      Tahata, K., Tomizawa, S.
    • Journal Title

      Journal of Statistics : Advances in Theory and Applications 1

      Pages: 19-33

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ridit score type quasi-symmetry and decomposition of symmetry for square contingency tables with ordered categories2009

    • Author(s)
      Iki, K., Tahata, K., Tomizawa, S.
    • Journal Title

      Austrian Journal of Statistics 38

      Pages: 183-192

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Decomposition of diagonals-parameter symmetry model and orthogonality of its test statistic for square contingency tables2009

    • Author(s)
      Tahata, K., Tomizawa, S.
    • Journal Title

      Journal of Statistical Theory and Applications 8

      Pages: 406-415

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Orthogonal decomposition of point-symmetry for multi-way tables.2008

    • Author(s)
      Tahata K., Tomizawa, S.
    • Journal Title

      Advances in Statistical Analysis : Journal of the German Statistical Society Vol.92

      Pages: 255-269

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generalized marginal homogeneity model and its relation to marginal equimoments for square contingency tables.2008

    • Author(s)
      Tahata K., Tomizawa S.
    • Journal Title

      Advances in Data Analysis and Classification Vol.2

      Pages: 295-311

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A measure of linear diagonals-parameter symmetry for square contingency tables with ordered categories2008

    • Author(s)
      Kouji Yamamoto, Sadao Tomizawa
    • Journal Title

      Model assisted Statistics and Applications 3

      Pages: 239-252

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized marginal homogeneity model and its relation to Marginal equimoments for square contingency tables2008

    • Author(s)
      Kouji Tahata, Sadao Tomizawa
    • Journal Title

      Advances in Data Analysis and Classification 2

      Pages: 295-311

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized measure of departure from no three-factor Interaction model for 2x2xK contingency tables2008

    • Author(s)
      Kouji Yamamoto, Yohei Ban, Sadao Tomizawa
    • Journal Title

      Entropy : International and Interdisciplinary Journal of Entropy and Information Studies 10

      Pages: 776-785

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Improvement of measures of marginal homogeneity in square contingency tables.2011

    • Author(s)
      増村一穂,山本紘司,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2011-03-22
    • Related Report
      2010 Final Research Report
  • [Presentation] On expected mean squared error of estimators for symmetry in multi-way tables.2011

    • Author(s)
      井上貴博,田畑耕治,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2011-03-22
    • Related Report
      2010 Final Research Report
  • [Presentation] 正方分割表における二重対称性の分解2011

    • Author(s)
      田畑耕治,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2011-03-22
    • Related Report
      2010 Final Research Report
  • [Presentation] 順序カテゴリをもつ正方分割表における対称性の分解について2010

    • Author(s)
      田畑耕治,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-24
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 多元分割表における累積対称モデルに対する分解2010

    • Author(s)
      山本紘司,田畑耕治,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-24
    • Related Report
      2010 Final Research Report
  • [Presentation] 正方分割表における周辺オッズを用いた周辺同等性からの隔たりを測る尺度2010

    • Author(s)
      生亀清貴,田畑耕治,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-24
    • Related Report
      2010 Final Research Report
  • [Presentation] 分割表における準対称性からの隔たりを測る尺度2010

    • Author(s)
      田畑耕治,冨田聡人,富澤貞男
    • Organizer
      統計関連学会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2010-09-12
    • Related Report
      2010 Final Research Report
  • [Presentation] 分割表における対称準一様連関モデルとその分解2010

    • Author(s)
      山本紘司,富澤貞男
    • Organizer
      応用統計学会
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2010-05-24
    • Related Report
      2010 Final Research Report
  • [Presentation] 正方分割表における拡張リジット型準対称モデル2010

    • Author(s)
      生亀清貴,田畑耕治,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      慶応大学
    • Year and Date
      2010-03-26
    • Related Report
      2010 Final Research Report
  • [Presentation] 三元分割表における累積対称モデルからの隔たりを測る尺度2010

    • Author(s)
      山本紘司,田畑耕治,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      慶応大学
    • Year and Date
      2010-03-24
    • Related Report
      2010 Final Research Report
  • [Presentation] 正方分割表におけるリジット型準対称モデルを用いた対称モデルの分解2009

    • Author(s)
      生亀清貴,田畑耕治,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2010 Final Research Report
  • [Presentation] 三元分割表における二重対称モデルとその分解2009

    • Author(s)
      高橋文博,山本紘司,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2010 Final Research Report
  • [Presentation] Normal distribution type symmetry model for square tables.2009

    • Author(s)
      山本紘司,田畑耕治,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-25
    • Related Report
      2010 Final Research Report
  • [Presentation] Normal distribution type symmetry model for square tables2009

    • Author(s)
      山本紘司, 田畑耕治, 富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] 多元分割表における点対称モデルの分解2009

    • Author(s)
      田畑耕治,富澤貞男
    • Organizer
      統計関連学会
    • Place of Presentation
      同志社大学
    • Year and Date
      2009-09-12
    • Related Report
      2010 Final Research Report
  • [Presentation] 正方分割表における非対称性を測る尺度とその応用2009

    • Author(s)
      田畑耕治,山田章文,山本紘司,富澤貞男
    • Organizer
      応用統計学会
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2009-08-02
    • Related Report
      2010 Final Research Report
  • [Presentation] measure of departure from conditional marginal homogeneity for square tables2009

    • Author(s)
      田畑耕治,岩下登志也,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-28
    • Related Report
      2010 Final Research Report
  • [Presentation] 正方分割表におけるリジット型準対称モデル2009

    • Author(s)
      生亀清貴,田畑耕治,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-28
    • Related Report
      2010 Final Research Report
  • [Presentation] 順序カテゴリ分割表における縮小度を測る尺度2009

    • Author(s)
      山本紘司,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-28
    • Related Report
      2010 Final Research Report
  • [Presentation] 二元分割表における独立性の分解2008

    • Author(s)
      田畑耕治,宮本暢子,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-27
    • Related Report
      2010 Final Research Report
  • [Presentation] Measure of departure from linear diagonals-parameter symmetry for square tables.2008

    • Author(s)
      山本紘司,富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-27
    • Related Report
      2010 Final Research Report
  • [Presentation] Measure of departure from linear diagonals-parameter Symmetry for square tables2008

    • Author(s)
      山本紘司, 富澤貞男
    • Organizer
      日本数学会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-27
    • Related Report
      2008 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.rs.noda.tus.ac.jp/~stomizaw/

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://www.rs.noda.tus.ac.jp/~stomizaw/tomizawa/indexj.html

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.rs.noda.tus.ac.jp/~stomizaw/tomizawa/indexj.html

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.rs.noda.tus.ac.jp/~stomizaw/tomizawa/indexj.html

    • Related Report
      2008 Annual Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

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