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Assessing variation: a unifying approach for all scales of measurement


  • Tamar Gadrich


  • Emil Bashkansky


  • Ričardas Zitikis



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

    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. 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.
    3. 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. repec:spr:qualqt:v:51:y:2017:i:5:d:10.1007_s11135-016-0393-3 is not listed on IDEAS
    2. Klein, Ingo & Mangold, Benedikt, 2015. "Cumulative Paired ," FAU Discussion Papers in Economics 07/2015, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.


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