A Multiple Comparison Rank Sum Test: Treatments versus Control

Abstract

Problems of applied research have necessitated the investigation of multiple comparison procedures. Such investigations have been carried out almost entirely within the framework of the analysis of variance. Since the assumptions underlying the analysis of variance are not always valid, distribution-free or non-parametric procedures have been developed for data arising from a number of experimental designs. Most such procedures do not provide for multiple comparisons. This paper presents a rank sum multiple comparison test for comparing treatments with a control, when the data are from a one-way classification. Error rate is experimentwise. An experimentwise error rate is, by definition, the ratio of the number of experiments with one or more false significance statements to the total number of experiments. Thus, in computing this error rate, the experiment is the unit; the experiment which leads to a single false significance statement is rated no differently than the one in which all comparisons are falsely declared significant. If we set the error rate at a, then 1 a gives the probability that no false statements of significance will be made, in other words, that all statements will be correct when the null hypothesis is true. In an experiment where k independent comparisons are to be made, it is customary to use a