Assessing variation: a unifying approach for all scales of measurement

Tamar Gadrich (), Emil Bashkansky () and Ričardas Zitikis ()

Quality & Quantity: International Journal of Methodology, 2015, vol. 49, issue 3, 1145-1167

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

Keywords: Stevens classification system; Gini mean difference; Variability; Segregation; Integration; Enterprise risk management (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:qualqt:v:49:y:2015:i:3:p:1145-1167

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DOI: 10.1007/s11135-014-0040-9

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