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Decomposition of cumulative chi-squared statistics, with some new tools for their interpretation

Author

Listed:
  • Luigi D’Ambra

    (University of Naples, Via Cinthia, Monte Sant’Angelo)

  • Pietro Amenta

    (University of Sannio)

  • Antonello D’Ambra

    (University of Campania “L.Vanvitelli”)

Abstract

It is well known that the Pearson statistic $$\chi ^{2}$$ χ 2 can perform poorly in studying the association between ordinal categorical variables. Taguchi’s and Hirotsu’s statistics have been introduced in the literature as simple alternatives to Pearson’s chi-squared test for contingency tables with ordered categorical variables. The aim of this paper is to shed new light on these statistics, stressing their interpretations and characteristics, providing in this way new and different interpretations of these statistics. Moreover, a theoretical scheme is developed showing the links between the different proposals and classes of cumulative chi-squared statistical tests, starting from a unifying index of heterogeneity, unalikeability and variability measures. Users of statistics may find it attractive to understand well the different proposals. Some decompositions of both statistics are also highlighted. This paper presents a case study of optimizing the polysilicon deposition process in a very large-scale integrated circuit, to identify the optimal combination of factor levels. It is obtained by means of the information coming from a correspondence analysis based on Taguchi’s statistic and regression models for binary dependent variables. A new optimal combination of factor levels is obtained, different from many others proposed in the literature for this data.

Suggested Citation

  • Luigi D’Ambra & Pietro Amenta & Antonello D’Ambra, 2018. "Decomposition of cumulative chi-squared statistics, with some new tools for their interpretation," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 297-318, June.
    • Handle: RePEc:spr:stmapp:v:27:y:2018:i:2:d:10.1007_s10260-017-0401-3
    DOI: 10.1007/s10260-017-0401-3
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    References listed on IDEAS

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    1. Luigi D'Ambra & Onur Koksoy & Biagio Simonetti, 2009. "Cumulative correspondence analysis of ordered categorical data from industrial experiments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(12), pages 1315-1328.
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    Cited by:

    1. Antonello D’Ambra & Pietro Amenta & Anna Crisci & Antonio Lucadamo, 2022. "The generalized Taguchi’s statistic: a passenger satisfaction evaluation," METRON, Springer;Sapienza Università di Roma, vol. 80(1), pages 41-60, April.
    2. Todisco, Lucio & Tomo, Andrea & Canonico, Paolo & Mangia, Gianluigi & Sarnacchiaro, Pasquale, 2021. "Exploring social media usage in the public sector: Public employees' perceptions of ICT's usefulness in delivering value added," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
    3. Antonello D’Ambra & Pietro Amenta & Eric J. Beh, 2021. "Confidence regions and other tools for an extension of correspondence analysis based on cumulative frequencies," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 405-429, September.
    4. Herteliu, Claudiu & Jianu, Ionel & Dragan, Irina Maria & Apostu, Simona & Luchian, Iuliana, 2021. "Testing Benford’s Laws (non)conformity within disclosed companies’ financial statements among hospitality industry in Romania," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    5. D'Ambra, Luigi & Crisci, Anna & Meccariello, Giovanni & Della Ragione, Livia & Palma, Raffaela, 2021. "Evaluation of the social and economic impact of carbon dioxide (CO2) emissions on sustainable mobility using cumulative ordinal models: trend odds model," Socio-Economic Planning Sciences, Elsevier, vol. 75(C).
    6. Antonello D’Ambra & Pietro Amenta, 2023. "An extension of correspondence analysis based on the multiple Taguchi’s index to evaluate the relationships between three categorical variables graphically: an application to the Italian football cham," Annals of Operations Research, Springer, vol. 325(1), pages 219-244, June.

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