In this paper we develop theoretical criteria and econometric methods to rank policy interventions in terms of welfare when individuals are loss-averse. The new criterion for "loss aversion-sensitive dominance" defines a weak partial ordering of the distributions of policy-induced gains and losses. It applies to the class of welfare functions which model individual preferences with non-decreasing and loss-averse attitudes towards changes in outcomes. We also develop new statistical methods to test loss aversion-sensitive dominance in practice, using nonparametric plug-in estimates. We establish the limiting distributions of uniform test statistics by showing that they are directionally differentiable. This implies that inference can be conducted by a special resampling procedure. Since point-identification of the distribution of policy-induced gains and losses may require very strong assumptions, we also extend comparison criteria, test statistics, and resampling procedures to a partially-identified case. Finally, we illustrate our methods with an empirical application to welfare comparison of two income support programs.