SUMMARYThe 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. Copyright © 2011 John Wiley & Sons, Ltd.