This paper addresses the problematic nature of efforts in the law and the social and medical sciences to appraise the comparative circumstances of advantaged and disadvantaged groups on the basis of standard measures of differences in outcome rates, given that such measures tend to be systematically affected by the prevalence of an outcome. The rarer an outcome the greater tends to be the relative difference in experiencing it and the smaller tends to be the relative difference in avoiding it. Thus, for example, as mortality declines relative differences in mortality of advantaged and disadvantaged groups tend to increase while relative differences in survival tend to decrease; as procedures like immunization and cancer screening become more common, relative differences in rates of receipt of those procedures tend to decrease while relative differences in rates of failing to receive them tend to increase; relaxing mortgage lending criteria tends to increase relative differences in mortgage rejection rates while reducing relative differences in mortgage approval rates. Similarly, among subpopulations where adverse outcomes are comparatively rare (e.g., persons with high education or high income, British civil servants), relative differences in adverse outcomes tend to be larger, while relative differences in favorable outcomes tend to be smaller, than among subpopulations where adverse outcome are more common. Absolute differences between outcome rates and differences measured by odds ratios are unaffected by whether one examines the favorable or the adverse outcome. But such measures tend also to be affected by the overall prevalence of an outcome, though in a more complicated way than the two relative differences. Broadly, as uncommon outcomes become more common absolute differences tend to increase; as already common outcomes become even more common, absolute differences tend to decrease. Differences measured by odds ratios tend to change in the opposite direction of absolute differences as the prevalence of an outcome changes. The paper will explain these patterns and the misinterpretations of data on group differences arising from the failure to understand them. It will also describe a method for appraising the size of the difference in circumstances reflected by outcome rates of advantaged and disadvantaged groups that is theoretically unaffected by the prevalence of the outcome.