Open Conference Systems, 50th Scientific meeting of the Italian Statistical Society

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Cumulative chi-squared statistics for the service quality improvement. New properties and tools for its evaluation.
Antonello D'Ambra, Antonio Lucadamo, Pietro Amenta, Luigi D'Ambra

Last modified: 2018-05-17


In Customer Satisfaction survey one of the aim is to evaluate the relationships between a categorical dependent variable and one or more predictors. Correspondence Analysis and Non Symmetric Correspondence Analysis are useful statistical tools to graphically identify the nature of the association between two categorical items when a symmetric or asymmetric relationship is assumed. These techniques, based on Pearson chi-squared statistic and Goodman-Kruskal tau statistic respectively, can perform poorly when at least one of the variable has an ordinal structure. In this case it is more suitable the use of an index proposed by Taguchi. He introduced a measure that takes into account the presence of an ordinal categorical variable by considering the cumulative sum of cell frequencies in a contingency table, across this variable. This statistic performs better than Pearson’s chi-squared statistic and it is more appropriate when the number of categories is equal or larger than 5. The index is also at heart of a cumulative extension of correspondence analysis. In this paper we propose the use of a multiple version of Taguchi index, to study the relationship between a dependent ordinal variable and two predictors in service quality evaluation.

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