Using SAS to calculate tests of Cliff’s Delta

Abstract

This paper discusses a program that calculates three estimates for making statistical inferences regarding the delta statistic. The delta statistic (Cliff, 1993) may be used when testing null hypotheses about group differences on ordinal level measurements. This statistic and the inferential methods associated with it are addressed by considering data arranged in a dominance matrix. The program calculates the marginal values of the dominance matrix that are used in the inferential statistics associated with d (sample estimate of the population parameter). The three methods of inference for d include two estimates of the variance of d, and a confidence band around the sample value of d. The paper provides a demonstration of the SAS/IML code and examples of application of the code to simulation studies in statistics.