Because self-reported health status [SRHS] is an ordered response variable, inequality measurement for SRHS data requires a numerical scale for converting individual responses into a summary statistic. The choice of scale is however problematic, since small variations in the numerical scale may reverse the ordering of a given pair of distributions of SRHS data in relation to conventional inequality indices such as the variance. This paper introduces a parametric family of inequality indices, founded on an inequality ordering proposed by Allison and Foster [Allison, R.A., Foster, J., 2004. Measuring health inequalities using qualitative data. Journal of Health Economics 23, 505-524], which satisfy a suitable invariance property with respect to the choice of numerical scale. Several key members of the parametric family are also derived, and an empirical application using data from the Swiss Health Survey illustrates the proposed methodology. [Authors]