The performance of some tests of independence for contingency-type bivariate distributions

Abstract

SUMMARY Plackett (1965) has given a family of contingency-type bivariate distributions. We examine the Pitman efficiency of some tests of independence against alternatives of this kind. We find that the tests based on Spearman's rank correlation coefficient r s , Kendall's coefficient and on certain other measures are asymptotically equivalent. The asymptotic relative efficiency (ARE) of r S , relative to the ordinary correlation coefficient, is greater than or equal to 1. An example is constructed to show that the ARE can approach infinity. The ARE of R S compared to the coefficient of contingency is found to be 0-56.