By taking advantage of an experimental design which increases the number of observations per subject, the sensitivity of the proposed test is increased. In the first of a series of subexperiments, the score of a randomly selected experimentalS is ranked with the scores of the remaining (control) Ss, and the experimental S is discarded. This procedure is repeated until one S remains. The test criterion, Rn, is the sum of ranks of the experimental Ss; its exact sampling distribution, a normal approximation, and the sensitivity of the test relative to the Wilcoxon T, are described. Because of the large number of scores obtained, the test is particularly useful when preparing Ss is more costly than testing them, e.g., in tests following involved conditioning procedures. Since each S is discarded after experimental treatment, the test fills a real need in studies involving radiation, ablation, or other irreversible treatments.