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A note on the generalization of Rosenbaum's test for two-sample scale problem

Rosenbaum 12 proposed a distribution-free test for the two-sample scale problem based on a number of X-sample observations lying between the extremes of the Y-sample observations. We propose a distribution-free test for the two-sample scale problem; this test is resistant to possible outliers in both samples and generalizes the tests due to Rosenbaum 12 as well as a test due to Shetty and Bhat 7. The performance of the test is evaluated in terms of Pitman's asymptotic relative efficiency. An alternative expression in terms of ranks of ordered X-sample observations in the joint ranking of X and Y-sample observations is given to facilitate the computation of the test statistic and tabulate the upper cutoff points of the exact null distribution of the test statistic.