A test for second order stochastic dominance

In this paper we propose a test for second order stochastic dominance (SSD), for the case where both distribution functions are unknown. This is a generalization of a test proposed by Deshpande and Singh (1985), who compare a new random prospect with a known distribution function. We then show that our test is based on comparing the mean minus one half of Gini's mean difference of the distributions, which is known to be a necessary condition for SSD, as developed in the economics literature (Yitzhaki, 1982).