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An index for measuring departure from an anti-sum-symmetry model for square contingency tables with ordered categories Cover

An index for measuring departure from an anti-sum-symmetry model for square contingency tables with ordered categories

By: Shuji Ando  
Open Access
|Jan 2025

References

  1. Ando S. (2021a): Orthogonal decomposition of the sum-symmetry model for square contingency tables with ordinal categories: Use of the exponential sum-symmetry model. Biometrical Letters 58: 95–104.
  2. Ando S. (2021b): Orthogonal decomposition of the sum-symmetry model using the two-parameters sum-symmetry model for ordinal square contingency tables. Biometrical Letters 58: 105–117.
  3. Ando S. (2021c): An anti-sum-symmetry model and its orthogonal decomposition for ordinal square contingency tables with an application to grip strength test data. Biometrical Letters 58: 59–68.
  4. Ando S. (2022): Orthogonal decomposition of symmetry model using sum-symmetry model for ordinal square contingency tables. Chilean Journal of Statistics 13: 21–231.
  5. Ando S. (2023): Anti-sum-asymmetry models and orthogonal decomposition of anti-sum-symmetry model for ordinal square contingency tables. Austrian Journal of Statistics 52: 72–86.
  6. Ando S. (2024): Generalized sum-asymmetry model and orthogonality of test statistic for square contingency tables. Austrian Journal of Statistics 53: 99–108.
  7. Ando S., Fujimoto, K. and Tomizawa, S. (2024): A measure of departure from marginal homogeneity using continuation odds for square contingency tables with ordered categories. Sankhya B 86: 311–332.
  8. Ando S., Momozaki T., Masusaki Y. and Tomizawa S. (2024): An index for measuring degree of departure from symmetry for ordinal square contingency tables. Journal of the Korean Statistical Society 53: 883–905.
  9. Ando S., Noguchi T., Ishii A. and Tomizawa S. (2021): A two-dimensional index for marginal homogeneity in ordinal square contingency tables. SUT Journal of Mathematics 57: 211–224.
  10. Ando S., Tahata K. and Tomizawa S. (2017): Visualized measure vector of departure from symmetry for square contingency tables. Statistics in Biopharmaceutical Research 9: 212–224.
  11. Bishop Y. M., Fienberg S. E. and Holland P. W. (2007): Discrete Multivariate Analysis: Theory and Practice. Springer, New York.
  12. Bowker A. H. (1948): A test for symmetry in contingency tables. Journal of the American Statistical Association 43: 572–574.
  13. Iki K., Tahata K. and Tomizawa S. (2012): Measure of departure from marginal homogeneity using marginal odds for multi-way tables with ordered categories. Journal of Applied Statistics 39: 279-295.
  14. Intage group self-designed survey. (2023, January 27). Intage Siru gallery (in Japanese). https://gallery.intage.co.jp/smartphone-operation/
  15. McCullagh P. (1978): A class of parametric models for the analysis of square contingency tables with ordered categories. Biometrika 65: 413–418.
  16. Stuart A. (1955): A test for homogeneity of the marginal distributions in a two-way classification. Biometrika 42: 412–416.
  17. Tahata K., Iwashita T. and Tomizawa S. (2006): Measure of departure from symmetry of cumulative marginal probabilities for square contingency tables with ordered categories. SUT Journal of Mathematics 42: 7–29.
  18. Tahata K., Iwashita T. and Tomizawa S. (2008): Measure of departure from conditional marginal homogeneity for square contingency tables with ordered categories. Statistics 42: 453–466.
  19. Tahata K., Tajima K. and Tomizawa S. (2006): A measure of asymmetry of marginal ridits for square contingency tables with ordered categories. Journal of the Japanese Society of Computational Statistics 19: 69–85.
  20. Tomizawa S. (1984): Three kinds of decompositions for the conditional symmetry model in a square contingency table. Journal of the Japan Statistical Society 14: 35–42.
  21. Tomizawa S. (1993): Diagonals-parameter symmetry model for cumulative probabilities in square contingency tables with ordered categories. Biometrics 49: 883–887.
  22. Tomizawa S. and Makii T. (2001): Generalized measures of departure from marginal homogeneity for contingency tables with nominal categories. Journal of Statistical Research 35: 1–24.
  23. Tomizawa S., Miyamoto N. and Hatanaka Y. (2001): Measure of asymmetry for square contingency tables having ordered categories. The Australian and New Zealand Journal of Statistics 43: 335–349.
  24. Tomizawa S., Miyamoto N. and Ashihara N. (2003): Measure of departure from marginal homogeneity for square contingency tables having ordered categories. Behaviormetrika 30: 173–193.
  25. Tomizawa S., Seo T. and Yamamoto H. (1998): Power-divergence-type measure of departure from symmetry for square contingency tables that have nominal categories. Journal of Applied Statistics 25: 387–398.
  26. Yamamoto K., Aizawa M. and Tomizawa S. (2016): Measure of departure from sum-symmetry model for square contingency tables with ordered categories. Journal of Statistics: Advances in Theory and Applications 16: 17–43.
  27. Yamamoto K., Tanaka Y. and Tomizawa S. (2013): Sum-symmetry model and its orthogonal decomposition for square contingency tables. SUT Journal of Mathematics 49: 121–128.
DOI: https://doi.org/10.2478/bile-2024-0007 | Journal eISSN: 2199-577X | Journal ISSN: 1896-3811
Language: English
Page range: 101 - 113
Published on: Jan 9, 2025
Published by: Polish Biometric Society
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2025 Shuji Ando, published by Polish Biometric Society
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.