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Explorative Data Analysis and CATANOVA for Ordinal Variables: An Integrated Approach

Author

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  • Pasquale Sarnacchiaro
  • Antonello D'ambra

Abstract

Categorical analysis of variance (CATANOVA) is a statistical method designed to analyse variability between treatments of interest to the researcher. There are well-established links between CATANOVA and the τ statistic of Goodman and Kruskal which, for the purpose of the graphical identification of this variation, is partitioned using singular value decomposition for Non-Symmetrical Correspondence Analysis (NSCA) (D'Ambra & Lauro, 1989). The aim of this paper is to show a decomposition of the Between Sum of Squares (BSS), measured both in CATANOVA framework and in the statistic τ, into location, dispersion and higher order components. This decomposition has been developed using Emerson's orthogonal polynomials. Starting from this decomposition, a statistical test and a confidence circle have been calculated for each component and for each modality in which the BSS was decomposed, respectively. A Customer Satisfaction study has been considered to explain the methodology.

Suggested Citation

  • Pasquale Sarnacchiaro & Antonello D'ambra, 2007. "Explorative Data Analysis and CATANOVA for Ordinal Variables: An Integrated Approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(9), pages 1035-1050.
    • Handle: RePEc:taf:japsta:v:34:y:2007:i:9:p:1035-1050
    DOI: 10.1080/02664760701591937
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    Citations

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    Cited by:

    1. Ida Camminatiello & Antonello D’Ambra & Luigi D’Ambra, 2022. "The association in two-way ordinal contingency tables through global odds ratios," METRON, Springer;Sapienza Università di Roma, vol. 80(1), pages 9-22, April.
    2. Pasquale Sarnacchiaro & Antonello D’Ambra & Luigi D’Ambra, 2016. "CATANOVA for ordinal variables using orthogonal polynomials with different scoring methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(13), pages 2490-2502, October.
    3. Rosaria Lombardo & Eric Beh & Antonello D'Ambra, 2011. "Studying the dependence between ordinal-nominal categorical variables via orthogonal polynomials," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(10), pages 2119-2132.

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