title: Wilcoxon's signed-rank statistic: what null hypothesis and why it matters.
abstract: 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.
authors.affiliation: Center for Devices and Radiological Health, US Food and Drug Administration, Silver Spring, MD, 20993, USA.
authors.forename: Heng
authors.initials: H
authors.lastname: Li
authors.forename: Terri
authors.initials: T
authors.lastname: Johnson
mesh_terms: D006801:Humans; D011897:Random Allocation; D018709:Statistics, Nonparametric
keywords: matched-pairs design; one-sample t-test; pedagogy; sign test