Comments on “the Simplest Signed-Rank Tests”

Abstract

In a fundamental contribution, Tukey [5] showed that the Wilcoxon signed-rank test [14, 15, 16, 17] is equivalent to a subclass of some tests presented by Walsh [7, 8]. Since Tukey's memorandum did not explicitly state that only a subclass of Walsh's tests is involved, misunderstandings seem to have arisen concerning the extent of the equivalence between these two classes of tests. This paper points out that a large proportion of Walsh's results are not equivalent to Wilcoxon signed-rank tests, and that some of these nonequivalent results have useful properties, which can be exploited to obtain tests and confidence intervals having increased validity, increased efficiency, additional probability levels, or requiring less computation, compared to the Wilcoxon signed-rank results.