This paper provides an examination of the notion of “distance” and ordering between the whole distributions of earnings for men and women, and some related counterfactuals.We investigate aggregative measures and their statistical implementation and evaluation. We provide a synthesis of the decision theoretic basis of measures for such things as the “gender gap”. “Strong” comparison/ordering of distributions of outcomes requires subjective evaluation functions reflecting decision maker’s preferences. Examples include popular notions of the “gender gap” based on means or medians. These are seen to be supported by rather strong subjective evaluation of heterogenous outcomes at different quantiles. We examine a more flexible and well supported distribution metric based on entropies. We then examine complementary (weak) uniform ranking of distributed outcomes over large classes of preferences by such methods and tests as stochastic dominance. The paper’s primary purpose is to provide a comprehensive application of these two interrelated approaches based on the most popular data and models in the existing literature for the US labor market for the last several decades. Selection to the labor force is a major issue and requires new techniques for its treatment at the entire distribution level, compared to existing approaches to the conditional mean and median. We adopt a new quantile-copula approach to modeling the participation decision and find selection is consequential for a deeper understanding of the “gap” and its movement over the economic cycle. We also provide decomposition of the gap to market pricing effects and human characteristic effects based on counterfactual distributions derived from the conditional quantiles.