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a non-parametric rank test to compare two paired samples, whether values in one are bigger than in the other. This test is NOT the same as the sign test.

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Why is the asymptotic relative efficiency of the Wilcoxon test $3/\pi$ compared to Student's...

Brief sketch of ARE for one-sample $t$-test, signed test and the signed-rank test I expect the long version of @Glen_b's answer includes detailed analysis for two-sample signed rank test along with t …
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