Summary
As a test for the hypothesis of equality of means in a sample ofn matched pairs of observations from a single bivariate population in(x, y), Wilcoxon ([4], [5]) proposed a signed rank sum testU involving the differencesz=x\t-y. Tables of valuesUs have been provided forn of 50 or less and four significance levelsε. The following paper considers some generalizations of the Wilcoxon test for the case of matched bivariate or trivariate populations. These tests utilize certain properties of thep-variate normal distribution when integrated over certain regions for the cases:p=2,3.
Similar content being viewed by others
References
B. M. Bennett, “On multivariate sign tests,”J- R- Statist. Soc. B, 24 (1962), 159–161.
M. G. Kendall,Rank Correlation Methods, 3rd edition. Griffin & Co. Ltd., 1962.
M. G. Kendall and A. Stuart,Advanced Theory of Statistics, I, Griffin & Co. Ltd., 1962.
F. Wilcoxon, “Individual comparisons by ranking methods,”Biometrics Bulletin, 1 (1945), 80–82.
F. Wilcoxon, “Probability tables for individual comparisons by ranking methods,”Biometrics, 3 (1947), 119–122.
F. Wilcoxon, S. K. Katti and R. A. Wilcox,Critical Values and Probability Levels for the Wilcoxon Rank Sum Test and the Signed Rank Test, Lederle Laboratories and Florida State University, 1963.
About this article
Cite this article
Bennett, B.M. On multivariate signed rank tests. Ann Inst Stat Math 17, 55–61 (1965). https://doi.org/10.1007/BF02868152
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02868152