Assessing Variation: a Unifying Approach for All Scales of Measurement

• Activity Number: 133
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Quality and Productivity Section
• Author(s): Emil Bashkansky*+ and Tamar Gadrich and Ricardas Zitikis
• Companies: ORT Braude College of Engineering and ORT Braude College of Engineering and University of Western Ontario
• Keywords: intra variability ; inter variability ; segregation ; integration ; enterprise risk management ; measurement scale

Abstract

For various reasons quite often do we wish to assess the variability of populations or their samples. These are complex tasks due to various reasons, not least because of the usual heterogeneity of populations, which can be made up of various groups and categories often requiring different scales of measurement. A number of measures of variability have been developed to accommodate various scales of measurement: nominal, ordinal, interval and ratio. This variety of scales with their different restrictions on possible arithmetical operations and order relationships carries serious challenges for researchers and decision makers, in particular for those working in areas such as quality engineering and management, or enterprise risk management (ERM) where measurements on different scales need to be aggregated into one generalized or enterprise-wide metric. 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 suggest several indices of segregation. General considerations are illustrated on real-life and artificial data sets.