Nonparametric Tests for Intransitivity in Multiple Samples TOM HETTMANSPERGER Penn State University The standard nonparametric test for comparing three samples is the Kruskal-Wallis test.  The Kruskal-Wallis statistic can be written as a quadratic form in the three pairwise Mann-Whitney statistics.  The vector of Mann-Whitney statistics has a nonsingular covariance matrix and, hence, a full rank quadratic form, Q.  The quadratic form Q can be decomposed into the Kruskal-Wallis statistic and another quadratic form C with 1 degree of freedom.  The quadratic form C measures the degree of intransitivity in the data.  We will demonstrate how intransitivity can arise and illustrate the nature of C.  We will also discuss the asymptotic distribution of C.