Wilcoxon's signed‐rank statistic: what null hypothesis and why it matters

In statistical literature, the term 'signed-rank test' (or 'Wilcoxon signed-rank test') has been used to refer to two distinct tests: a test for symmetry of distribution and a test for the median of a symmetric distribution, sharing a common test statistic. To avoid potential ambiguity, we propose to refer to those two tests by different names, as 'test for symmetry based on signed-rank statistic' and 'test for median based on signed-rank statistic', respectively. The utility of such terminological differentiation should become evident through our discussion of how those tests connect and contrast with sign test and one-sample t-test. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.