Atkinson (1987) proposed stochastic dominance criteria for analysing poverty which, under certain conditions, establish orderings of states for any poverty line and any poverty measure within given class, refocusing debate on the nature of the income distribution of the poor. Employing new empirical techniques, these criteria are implemented for the United States from 1970 to 1990 using the Panel Study of Income Dynamics. Results highlight the pivotal role of family size scale economies in consumption, indicate different experiences for white versus non-white groups and suggest that optimism over the progress of the poor is not warranted.