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

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.