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

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