Assessing variation: a unifying approach for all scales of measurement

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 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

Assessing variation: a unifying approach for all scales of measurement

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Publisher
Springer Netherlands
Copyright
Copyright © 2014 by Springer Science+Business Media Dordrecht
Subject
Social Sciences, general; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1007/s11135-014-0040-9
Publisher site
See Article on Publisher Site

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.

Journal

Quality & QuantitySpringer Journals

Published: Jun 1, 2014

References

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