Testing for independence: Saddlepoint approximation to associated permutation distributions

Abstract

One of the most popular class of tests for independence between two random variables is the general class of rank statistics which are invariant under permutations. This class contains Spearman’s coefficient of rank correlation statistic, Fisher-Yates statistic, weighted Mann statistic and others. Under the null hypothesis of independence these test statistics have a permutation distribution that is usually approximated by using asymptotic normal theory to determine p-values for these tests. In this note we suggest using a saddlepoint approach that is almost exact and needs no simulations in order to calculate the p-value for tests in this class.