Cumulative chi-squared statistics for the service quality improvement: new properties and tools for the evaluation

Abstract

In service quality evaluation, data are often categorical variables with ordered categories and collected in two way contingency table. The Taguchi’s statistic is a measure of the association between these variables as a simple alternative to Pearson’s test. An extension of this statistic for three way contingency tables handled in two way mode is introduced.We highlight its several properties, the approximated distribution, a decomposition according to orthogonal quantities reflecting the main effects and the interaction terms, and an extension of cumulative correspondence analysis based on it