On the sampling distribution of swap-rate

When we are to select students using the result of an entrance examination, it is common to select N0 students out of N applicants on the basis of a composite score of m subtests, where N0, the number of students to be selected, is determined prior to the administration of the entrance examination. The swap-rate is an intuitively easy-to-understand measure of the contribution of each subtest to the selection. The swap-rate of the j-th test is defined as the proportion, to N0, of the number of students who failed to pass the examination if the j-th test is not used for the selection. In this paper we first discuss the sampling distribution of the swap-rate under the normality assumption and then show the result of a bootstrapping using real selection data.