Introduction to Wilcoxon (1945) Individual Comparisons by Ranking Methods

Abstract

When in 1945, Frank Wilcoxon published this unpretentious little paper, he could hardly have guessed that the two techniques he was proposing would soon occupy a central place in a newly developing branch of statistics that became known as nonparametrics. Wilcoxon (1892–1965) a physical chemist by training who was employed by the American Cyanamid Company in Stamford, Connecticut, came to statistics because of a need for analyzing laboratory data. His main motivation in developing the two new techniques seems to have been a desire to replace the endless t-statistics that he needed for the analysis of his laboratory measurements by something computationally simpler. In a subsequent publication [Wilcoxon (1949)], he explained

It is not always realized that there are available rapid approximate methods which are quite useful in interpreting the results of experiments, even though these approximate methods do not utilize fully the information contained in the data.

The two procedures, now generally known as the Wilcoxon rank sum test (or two-sample test) and the Wilcoxon signed rank test (or one-sample test), are used for the comparison of two treatments involving unpaired and paired sample observations, respectively. In classical normal theory statistics, two treatments are compared with the help of appropriate t-tests. Wilcoxon proposed replacing the actual data values by their ranks to simplify computational effort.