On unit free assessment of the extent of multilateral distributional variation

Abstract

Summary Multilateral comparison of outcomes drawn from multiple groups pervade the social sciences and measurement of their variability, usually involving functions of respective group location and scale parameters, is of intrinsic interest. However, such approaches frequently mask more fundamental differences that more comprehensive examination of relative group distributional structures reveal. Indeed, in categorical data contexts, location- and scale-based techniques are no longer feasible without artificial and questionable cardinalisation of categories. Here, Gini’s transvariation measure is extended and employed in providing quantitative and visual multilateral comparison tools in discrete, continuous, categorical, univariate, or multivariate settings which are particularly useful in paradigms where cardinal measure is absent. Two applications, one analysing Eurozone cohesion in terms of the convergence or divergence of constituent nations income distributions, the other, drawn from a study of ageing, health, and income inequality in China, exemplify their use in a continuous and categorical data environment.