Analysis of Variance of Categorical Data

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2022 by IJMTT Journal
Volume-68 Issue-9
Year of Publication : 2022
Authors : Khaled Fattah Sheet, Khawla Musta Sadiq
 10.14445/22315373/IJMTT-V68I9P503

How to Cite?

Khaled Fattah Sheet, Khawla Musta Sadiq, "Analysis of Variance of Categorical Data," International Journal of Mathematics Trends and Technology, vol. 68, no. 9, pp. 11-15, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I9P503.

Abstract
The present study focuses on analysis of variance of categorical data. So, it was noted that contingency tables are often subjected to the analysis of variance (abbreviated hereafter as ANOVA), using the so-called log linear model. Some references were also provided. The current study applied dual scaling to ANOVA of categorical date. One natural question is whether or is not dual scaling is any better than the log linear approach. Therefore, there does not seem to be any comparative study available, and hence our discussion must remind speculative.

Keywords : Analysis, mathematics, Variance, Dual scaling.

Reference

[1] Aitkin, M, “Analysis of Categorical Date Dual Scaling and Its Applications,“ Royal Statistical Society Journal Series A, vol.145, pp.513–516, 1982.
[2] Anderberg, M, “Cluster Analysis for Applications,” 1973.
[3] Benzecri, J. P, “Correspondence Analysis Handbook,” Macel Dekker.
[4] Benali, H, “Stability of Factorial Analysis of Multiple Correspondences in the Event of Missing Data and Modalities With Small Numbers,” Doctoral Dissertation, INRIA),1986.
[5] Benzécri, J. P, “Validity of Assessment Scales In Psychology and Psychiatry and Psychosocial Correlations,” Cahiers De L’analyse Des Données, vol.1, no.17, pp.55–86, 1992.
[6] Blasius, J., & Greenacre, M. (Eds. ), Visualization and Verbalization of Data. CRC Press, 2014.
[7] Bock, H. H, “Probabilistic Models In Cluster Analysis,” Computational Statistics & Data Analysis, vol.1, no.3, pp.5–28, 1996.
[8] Carman, J. M, “Consumer Perceptions of Service Quality,” An Assessment of T. Journal of Retailing, vol.1, no.66, pp.33, 1990.
[9] Chazal, F., & Michel, B, “An Introduction to topological Data Analysis,” Fundamental and Practical Aspects for Data Scientists, 2017.
[10] Cooksey, R. W, “The Methodology of Social Judgement Theory,” Thinking & Reasoning, vol.3, no.21, pp.141–174, 1996.
[11] Fisher, R. A, “The Precision of Discriminant Functions,” Annals of Eugenics, vol.1, no.10, pp.422–429, 1940.
[12] Greenacre, M, “ Correspondence Analysis In Practice,” In Hapman and Hall/Crc, 2017.
[13] Guttman, L, “An Approach for Quantifying Paired Comparisons and Rank Order,” The Annals of Mathematical Statistics, vol.17, no.2, pp.144–163, 1946.
[14] Li, V. O., & Qiu, X, “Personal Communication Systems (PCS,” Proceedings of the IEEE, vol.9, no.83, pp.1210–1243, 1995.
[15] Meulman, J. J, “ Optimal Scaling Methods for Multivariate Categorical Data Analysis,” SPSS White Paper . : Chicago, 1988.
[16] Mucha, H. J, “ Improvement of Stability in Cluster Analysis and Principal Components Analysis By Special Weighting the Variables,” In Operations Research, vol.91, pp.351-354, 1992. Physica-Verlag HD.
[17] Mullet, G. M, “ Correspondence Analysis: A New tool for Image Studies,” Journal of Professional Services Marketing , vol.3, no.2, pp.44 –14, 1987.
[18] Nishisato, S., & Ahn, H, “ When not to Analyze Data: Decision Making on Missing Responses In Dual Scaling ,” Annals of Operations Research, vol.2, no.55, pp.361–378, 1995.
[19] Nishisato, S., & Clavel, J. G, “ A note on Between-Set Distances In Dual Scaling and Correspondence Analysis,” Behaviormetrika, vol.1, no.30, pp.87–98, 2003.
[20] Nishisato, S., & Gaul, W, “ Marketing Data Analysis By Dual Scaling,” International Journal of Research In Marketing, vol.3, no.5, pp.151–170, 1988.
[21] Nishisato, S., & Sheu, W. J, “A note on Dual Scaling of Successive Categories Data,” Psychometrika, vol.4, no.49, pp.493–500, 1984.
[22] Nishisato, S, “Graphical Representation of Quantified Categorical Data: Its Inherent Problems,”Journal of Statistical Planning and Inference, vol.1–2, no.43, pp.121–132, 1995a.
[23] Nishisato, S, “ Ptimization and Data Structure: Seven Faces of Dual Scaling,” Annals of Operations Research, vol.2, no.55, pp.345– 359, 1995b.
[24] Nishisato, S, “ Gleaning In the Field of Dual Scaling,” Psychometrika, vol.4, no.61, pp.559–599, 1996.
[25] Ogasawara, H, “ Oblique Factors and Components With Independent Clusters,” Psychometrika, vol.2, no.68, pp.299–32, 2003.
[26] Padberg, M. W., Van Roy, T. J., & Wolsey, L. A, “Valid Linear Inequalities for Fixed Charge Problems,” Operations Research, vol.4, no.33, pp.842–861, 1985.
[27] Sharma, R., Joshi, S., Singh, K. D., & Kumar, A, “Visual Evoked Potentials: normative Values and Gender Differences,” Journal of Clinical and Diagnostic Research: JCDR, vol.7, no.12, pp.CC12, 2015.