Assessing variation: a unifying approach for all scales of measurement
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 discu...
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| Veröffentlicht in: | Quality & quantity 2015-05, Vol.49 (3), p.1145-1167 |
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| creator | Gadrich, Tamar Bashkansky, Emil Zitikis, Ričardas |
| description | 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. |
| doi_str_mv | 10.1007/s11135-014-0040-9 |
| format | Article |
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| subjects | Certainty Decision making Decomposition Economic theory Educational institutions Enterprise risk management Management Mathematical models Measurement Measures of variability Methodology of the Social Sciences Propositions Risk Risk management Segregation Social Sciences Studies Uncertainty |
| title | Assessing variation: a unifying approach for all scales of measurement |
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