摘要：For two independent random variables, X and Y , let p = P(X >Y )+0:5P(X = Y ), which is sometimes described as a probabilistic measureof e ect size. It has been argued that for various reasons, p represents animportant and useful way of characterizing how groups di er. In clinicaltrials, for example, an issue is the likelihood that one method of treatmentwill be more e ective than another. The paper deals with making inferencesabout p when three or more groups are to be compared. When tied valuescan occur, the results suggest using a multiple comparison procedure basedon an extension of Cli 's method used in conjunction with Hochberg's sequentiallyrejective technique. If tied values occur with probability zero, analternative method can be argued to have a practical advantage. As for aglobal test, extant rank-based methods are unsatisfactory given the goal ofcomparing groups based on p. The one method that performed well in simulationsis based in part on the distribution of the di erence between eachpair of random variables. A bootstrap method is used where a p-value isbased on the projection depth of the null vector relative to the bootstrapcloud. The proposed methods are illustrated using data from an interventionstudy.
