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Assessing variation: a unifying approach for all scales of measurement

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  • Tamar Gadrich
  • Emil Bashkansky
  • Ričardas Zitikis

Abstract

Recent developments in the area of enterprise risk management, especially in the context of high impact events, their uncertainty and variability, have highlighted the need for developing a unified approach for variability measurement in qualitative and quantitative phenomena. In this paper we discuss such an approach, which is based on Gini’s seminal ideas and applicable for all types of data: nominal, ordinal, interval, and ratio. By establishing a general total-variation decomposition theorem, we provide a tool for decomposing the total variation into within (intra) and between (inter) components, and as a consequence introduce several indices of interest. We illustrate our general considerations using specially designed artificial data-sets as well as real-life examples pertaining to countries, their territorial units, and educational institutions. Copyright Springer Science+Business Media Dordrecht 2015

Suggested Citation

  • Tamar Gadrich & Emil Bashkansky & Ričardas Zitikis, 2015. "Assessing variation: a unifying approach for all scales of measurement," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 1145-1167, May.
    • Handle: RePEc:spr:qualqt:v:49:y:2015:i:3:p:1145-1167
    DOI: 10.1007/s11135-014-0040-9
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    References listed on IDEAS

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    1. Yau, Sheena & Kwon, Roy H. & Scott Rogers, J. & Wu, Desheng, 2011. "Financial and operational decisions in the electricity sector: Contract portfolio optimization with the conditional value-at-risk criterion," International Journal of Production Economics, Elsevier, vol. 134(1), pages 67-77, November.
    2. D Wu & D L Olson, 2010. "Enterprise risk management: coping with model risk in a large bank," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(2), pages 179-190, February.
    3. Giovanni Maria Giorgi, 2005. "Gini's scientific work: an evergreen," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-315.
    4. Wu, Desheng Dash & Olson, David L. & Birge, John R., 2011. "Introduction to special issue on "Enterprise risk management in operations"," International Journal of Production Economics, Elsevier, vol. 134(1), pages 1-2, November.
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    Cited by:

    1. Yariv N. Marmor & Emil Bashkansky, 2024. "Reliability of Partitioning Metric Space Data," Mathematics, MDPI, vol. 12(4), pages 1-18, February.
    2. Stefania Capecchi & Domenico Piccolo, 2017. "Dealing with heterogeneity in ordinal responses," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(5), pages 2375-2393, September.
    3. Amalia Vanacore & Maria Sole Pellegrino, 2022. "A weighted distance metric for assessing ranking dissimilarity and inter-group heterogeneity," METRON, Springer;Sapienza Università di Roma, vol. 80(2), pages 175-185, August.
    4. Vanacore, Amalia & Pellegrino, Maria Sole, 2021. "Testing inter-group ranking heterogeneity: do patient characteristics matter for prioritization of quality improvements in healthcare service?," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
    5. Vladimir Turetsky & Emil Bashkansky, 2022. "Ordinal response variation of the polytomous Rasch model," METRON, Springer;Sapienza Università di Roma, vol. 80(3), pages 305-330, December.
    6. Raquel González del Pozo & Luis C. Dias & José Luis García-Lapresta, 2020. "Using Different Qualitative Scales in a Multi-Criteria Decision-Making Procedure," Mathematics, MDPI, vol. 8(3), pages 1-20, March.
    7. Amalia Vanacore & Maria Sole Pellegrino, 2019. "Checking quality of sensory data via an agreement-based approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(5), pages 2545-2556, September.
    8. Klein, Ingo & Mangold, Benedikt, 2015. "Cumulative Paired 𝜙-Entropy," FAU Discussion Papers in Economics 07/2015, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.

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