A Class of Distribution-Free Two-Sample Tests Based on Placements

We consider a class of two-sample distribution-free tests that are appropriate for situations where one of the sample sizes is large relative to the other. These procedures are based on the placements of the observations in the smaller sample among the ordered observations in the larger sample, and this class of tests generalizes the Mann-Whitney (1947) procedure in much the same way that the class of linear rank tests generalizes the equivalent Wilcoxon (1945) rank sum form. Optimality criteria for choosing a test from this class are discussed and limiting distributions for the associated class of test statistics are determined for the case where only one of the sample sizes goes to infinity.