Stochastic dominance criteria are commonly used to draw welfare-theoretic inferences about comparisons of income distribution as well as ranking probability distributions in the analysis of choice under uncertainty. However, just as some measures of location and dispersion can be catastrophically sensitive to extreme values in the data it is also possible that conclusions drawn from empirical implementations of dominance criteria are unduly influenced by data contamination. We show the conditions under which this may occur for a number of standard dominance tools used in welfare analysis.