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Working paper 757

Gordon Anderson, "A Coefficient of Variation for Multivariate Ordered Categorical Outcomes.", 2023-09-05
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Abstract: Comparing the relative variation of ordinal variates defined on diverse populations is challenging. Pearsons’ Coefficient of Variation or its inverse (the Sharpe Ratio), each used extensively for comparing relative variation or risk tempered location in cardinal paradigms, cannot be employed in ordinal data environments unless cardinal scale is attributed to ordered categories. Unfortunately, due to the scale dependencies of the Coefficient of Variations denominator and numerator, such arbitrary attribution can result in equivocal comparisons. Here, based upon the notion of probabilistic distance, unequivocal, scale independent, Coefficient of Variation and Sharpe Ratio analogues for use with Multivariate Ordered Categorical Data are introduced and exemplified in an analysis of Canadian Human Resource distributions.

Keywords: ordinal outcomes, variation coefficient, Sharpe Ratio

JEL Classification: C18;I32;G10