Inferring inequality: Testing for median-preserving spreads in ordinal data

The median-preserving spread (MPS) ordering for ordinal variables has become ubiquitous in the inequality literature. We devise statistical tests of the hypothesis that a distribution G is not an MPS of a distribution F. Rejecting this hypothesis enables the conclusion that G is more unequal than F according to the MPS criterion. Monte Carlo simulations and novel graphical techniques show that a simple, asymptotic Z test is sufficient for most applications. We illustrate our tests with two applications: happiness inequality in the US and self-assessed health in Europe.