A coefficient of variation for ordered categorical data: Analyzing relative health inequality and ageing in the UK and relative human resource inequality and gender in Canada - Gordon Anderson (Institute for Fiscal Studies (IFS), 2023)
The burgeoning use of ordinal data throughout the Empirical Sciences calls for location and variation measurement instruments suitable for such data environments. Neither Pearson's Coefficient of Variation nor the Sharpe Ratio, relative variation comparison workhorses in cardinal worlds, are applicable in ordinal paradigms without artificial data scaling, a practice recently much criticized for its inherent ambiguity. Here, employing the concept of probabilistic distance, unequivocal, scale independent, Coefficient of Variation analogues for use in Multivariate Ordered Categorical environments are introduced and exemplified in analyses of Self-Reported Health outcomes in the UK and Human Resource determinants in Canada.
Keywords: C18; I32; G10; 330; Ordinal Data; Coefficient of Variation; Sharpe Ratio; Probabilistic Distance