This paper introduces a new graphical tool: the mean deviation concentration curve. Using a unified approach, we derive the associated dominance conditions that identify robust rankings of absolute socioeconomic health inequality for all indices obeying Bleichrodt and van Doorslaer's (2006) principle of income-related health transfer. We also derive dominance conditions that are compatible with other transfer principles available in the literature. In order to make the identification of all robust orderings implementable using survey data, we discuss statistical inference for these dominance tests. To illustrate the empirical relevance of the proposed approach, we compare joint distributions of income and health-related behavior in the United States.