This paper introduces a concept of inequality comparisons with ordinal bivariate categorical data. In our model, one population is more unequal than another when they have common arithmetic median outcomes and the first can be obtained from the second by correlation-increasing switches and/or median-preserving spreads. For the canonical 2 × 2 case (with two binary indicators), we derive a simple operational procedure for checking ordinal inequality relations in practice. As an illustration, we apply the model to childhood deprivation in Mozambique.