This paper provides the tools and procedures for empirically implementing several dominance criteria for social welfare comparisons and broad income inequality comparisons. Dominance criteria are expressed in terms of vectors of quantile ordinates based on income shares or quantile means. Statistical properties of these sample ordinates are established that allow a framework for statistical inference on these vectors. And practical empirical criteria are forwarded for using formal statistical inference tests to reach conclusions about ranking social welfare and inequality between distributions. Examples include rank dominance, generalized Lorenz dominance, dominance with crossing Lorenz curves, and distributional distance dominance between income groups.
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