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We discuss two novel approaches to the classical two-sample problem. Ourstarting point are properly standardized and combined, very popular in severalareas of statistics and data analysis, ordinal dominance and receivercharacteristic curves, denoted by ODC and ROC, respectively. The proposed newcurves are termed the comparison curves. Their estimates, being weighted rankprocesses on (0,1), form the basis of inference. These weighted processes areintuitive, well-suited for visual inspection of data at hand, and are alsouseful for constructing some formal inferential procedures. They can be appliedto several variants of two-sample problem. Their use can help to improve someexisting procedures both in terms of power and the ability to identify thesources of departures from the postulated model. To simplify interpretation offinite sample results we restrict attention to values of the processes on afinite grid of points. This results in the so-called bar plots (B-plots) whichreadably summarize the information contained in the data. What is more, we showthat B-plots along with adjusted simultaneous acceptance regions provideprincipled information about where the model departs from the data. This leadsto a framework which facilitates identification of regions with locallysignificant differences.  We show an implementation of the considered techniques to a standardstochastic dominance testing problem. Some min-type statistics are introducedand investigated. A simulation study compares two tests pertinent to thecomparison curves to well-established tests in the literature and demonstratesthe strong and competitive performance of the former in many typicalsituations. Some real data applications illustrate simplicity and practicalusefulness of the proposed approaches. A range of other applications ofconsidered weighted processes is briefly discussed too.

ODC and ROC curves, comparison curves, and stochastic dominance