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This paper proposes a new adaptive procedure for analyzing paired data. The procedure uses a function of ordered absolute values of the differences to measure tail heaviness of the underlying distribution. The value of the measure is then used to choose an appropriate signed rank test. The new adaptive procedure is shown to preserve the size of the test at its nominal level for all continuous distributions and typically has nearly the same power as the best signed rank test for a wide range of distributions.

A new two stage adaptive nonparametric test for paired differences