The concentration index of a binary outcome revisited

The binary variable is one of the most common types of variables in the analysis of income-related health inequalities. I argue that while the binary variable has some unusual properties, it shares many of the properties of the ratio-scale variable and hence lends itself to both relative and absolute inequality analyses, albeit with some qualifications. I argue that criticisms of the normalization I proposed in an earlier paper, and of the use of the binary variable for inequality analysis, stem from a misrepresentation of the properties of the binary variable, as well as a switch of focus away from relative inequality to absolute inequality. I concede that my normalization is not uncontentious, but, in a way, that has not previously been noted.