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International Conference on Rough Sets and Knowledge Technology

RSKT 2010: Rough Set and Knowledge Technology pp 273–280Cite as

Residual Analysis of Statistical Dependence in Multiway Contingency Tables

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6401))

Abstract

A Pearson residual is defined as the residual between actual values and expected ones of each cell in a contingency table. This paper shows that this residual is represented as linear sum of determinants of 2 ×2, which suggests that the geometrical nature of the residuals can be viewed from grasmmanian algebra.

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References

  1. Everitt, B.: The Analysis of Contingency Tables, 2nd edn. Chapman & Hall/CRC, Boca Raton (1992)

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  2. Tsumoto, S.: Contingency matrix theory: Statistical dependence in a contingency table. Inf. Sci. 179(11), 1615–1627 (2009)

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  3. Tsumoto, S., Hirano, S.: Meaning of pearson residuals - linear algebra view. In: Proceedings of IEEE GrC 2007. IEEE press, Los Alamitos (2007)

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  4. Tsumoto, S., Hirano, S.: Contingency matrix theory ii: Degree of dependence as granularity. Fundam. Inform. 90(4), 427–442 (2009)

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  5. Tsumoto, S., Hirano, S.: Dependency and granularity indata. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and Systems Science, pp. 1864–1872. Springer, Heidelberg (2009)

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  6. Tsumoto, S., Hirano, S.: Statistical independence and determinants in a contingency table - interpretation of pearson residuals based on linear algebra. Fundam. Inform. 90(3), 251–267 (2009)

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Author information

Authors and Affiliations

  1. Department of Medical Informatics, Faculty of Medicine, Shimane University, 89-1 Enya-cho Izumo, 693-8501, Japan

    Shusaku Tsumoto & Shoji Hirano

Authors
  1. Shusaku Tsumoto
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  2. Shoji Hirano
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Editor information

Editors and Affiliations

  1. School of Computer and Information Technology, Beijing Jiaotong University, 100044, Beijing, China

    Jian Yu

  2. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco

  3. Department of Mathematics and Computing Science, Saint Mary’s University, B3H 3C3, Halifax, Nova Scotia, Canada

    Pawan Lingras

  4. Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, 400065, Chongqing, China

    Guoyin Wang

  5. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

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Tsumoto, S., Hirano, S. (2010). Residual Analysis of Statistical Dependence in Multiway Contingency Tables. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds) Rough Set and Knowledge Technology. RSKT 2010. Lecture Notes in Computer Science(), vol 6401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16248-0_41

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  • DOI: https://doi.org/10.1007/978-3-642-16248-0_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16247-3

  • Online ISBN: 978-3-642-16248-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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