This paper outlines a class of statistical procedures that permit testing of a broad range of multidimensional stochastic dominance hypotheses and, more generally, welfare hypotheses that rely upon multiple stochastic dominance conditions. We apply the procedures to data on income and leisure hours for individuals in Germany, the UK, and the USA. We find that no country first-order stochastically dominates the others in both dimensions for all years of comparison. Furthermore, while in general the USA stochastically dominates Germany and the UK with respect to income, in most periods Germany stochastically dominates with respect to leisure hours. Finally, we find evidence that bivariate poverty (which refers, for example, to the working poor, that is, those who have little leisure and low income) is lower in Germany than in either the UK or the USA. On the other hand, poverty comparisons between the UK and the USA are sensitive to the subpopulation of individuals considered.