On the Permutation Distribution of Independence Tests

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 usually the normal asymptotic theory used to approximate the p-values for these tests. In this note we suggest using a saddlepoint approach that almost exact and need no extensive simulation calculations to calculate the p-value of such class of tests.