The study revisits the properties of group differential (GD) measures and extends it to include monotonicity and policy sensitivity axioms. Imposing level sensitivity, which indicates that a given gap is worse off at higher (lower) level of attainment (failure), the study concurs that ‘simple difference’ and ‘simple ratio’ are the most basic GD measures for attainment and failure indicators, respectively. It proposes two new measures, one each for attainment and failure, which have certain advantages from a policy implication perspective. An empirical illustration has been provided by taking two indicators from Millennium Development Goals for different regions of the world. Copyright © 2013 John Wiley & Sons, Ltd.