Ramses H. Abul Naga and Tarik Yalcin

Published October 2010

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To date, inequality orderings for ordered response data are only suitable for comparing distributions that share a common median state. In this paper we propose a methodology for comparing distributions irrespective of their medians. We set out to do so by introducing a general pre-ordering and equivalence relation defined over distributions with different median responses, leading us naturally to derive a partial ordering over equivalence classes. We then discuss the implications of our results for the axiomatic derivation of inequality indices for ordered response data.