Research ArticleOpen AccessGoogle Scholar indexed
Measure of Departure from Point-Symmetry for the Analysis of Collapsed Square Contingency Tables
Department of Economics, Nihon University, Tokyo, Japan
Department of Economics, Nihon University, Tokyo, Japan
Department of Economics, Nihon University, Tokyo, Japan
- 1 Department of Economics, Nihon University, Tokyo, Japan
- 2 Department of Economics, Nihon University, Tokyo, Japan
- 3 Department of Economics, Nihon University, Tokyo, Japan
Open Journal of Statistics·Volume 11 (2021)·Pages 1062–1071·Published 29 November 2021·DOI10.4236/ojs.2021.116063
Copy link · social · email
Abstract
For square contingency tables with ordered categories, there may be some cases that one wants to analyze them by considering collapsed 3 × 3 tables with some adjacent categories combined in the original table. This paper con siders the point-symmetry model (Wall and Lienert, 1976) for collapsed tables and proposes a measure to represent the degree of departure from point-symmetry for collapsed tables. Also it gives approximate confidence interval for the proposed measure.
KeywordsCollapsed TableDiversity IndexMeasurePoint-SymmetryPower-Divergence
- Wall, K.D. and Lienert, G.A. (1976) A Test for Point-Symmetry in J-Dimensional Contingency-Cubes. Biometrical Journal, 18, 259-264.
- Yamamoto, K., Murakami, S. and Tomizawa, S. (2013) Point-Symmetry Models and Decomposition for Collapsed Square Contingency Tables. Journal of Applied Statistics, 40, 1446-1452. https://doi.org/10.1080/02664763.2013.786028
- Tomizawa, S., Yamamoto, K. and Tahata, K. (2007) An Entropy Measure of Departure from Point-Symmetry for Two-Way Contingency Tables. Symmetry: Culture and Science, 18, 279-297.
- Hashimoto, K. (1999) Class Structure in Modern Japan: Theory, Method and Quantitative Analysis. Toshindo Press, Tokyo. (In Japanese)
- Iki, K., Okada, M. and Tomizawa, S. (2018) An Extended Bivariate T-Distribution Type Symmetry Model for Square Contingency Tables. Open Journal of Statistics, 8, 249-257. https://doi.org/10.4236/ojs.2018.82015
- Balcha, A. (2020) Curve Fitting and Least Square Analysis to Extrapolate for the Case of COVID-19 Status in Ethiopia. Advances in Infectious Diseases, 10, 143-159. https://doi.org/10.4236/aid.2020.103015
- Cressie, N. and Read, T.R.C. (1984) Multinomial Goodness-of-Fit Tests. Journal of the Royal Statistical Society, Series B, 46, 440-464. https://doi.org/10.1111/j.2517-6161.1984.tb01318.x
- Read, T.R.C. and Cressie, N. (1988) Goodness-of-Fit Statistics for Discrete Multivariate Data. Springer-Verlag, New York. https://doi.org/10.1007/978-1-4612-4578-0
- Patil, G.P. and Taille, C. (1982) Diversity as a Concept and Its Measurement. Journal of the American Statistical Association, 77, 548-561. https://doi.org/10.1080/01621459.1982.10477845