Testing the Hypothesis of Independence Between Two Sets of Variates

The article compares five methods for testing the hypothesis of independence between two sets of variates. Two of the methods are new and based on straightforward generalizations of two robust measures of covariance recently appearing in the literature. Simulation results indicate that both of the new methods provide reasonably accurate control over the probability of a Type I error even with a relatively small sample size and extreme departure from normality. The usual likelihood ratio test is already known to be unsatisfactory, and results in this article indicate that the control over the probability of a Type I error can be even worse than indicated by previous investigations. The new procedures are based on robust measures reflecting the linear association between two random variables, so they provide an important alternative to rank based methods.