Abstract
Abstract : A class of nonparametric tests based on the third quadrant layer ranks has recently been studied by Woodworth in connection with the problem of testing for independence in a bivariate distribution. In the present work, exact one-sided rejection regions are tabulated for the normal score layer rank test which is asymptotically locally most powerful for positive dependence in the bivariate normal distribution. The cut-off points are tabulated for sample sizes n=4(1)9 and significance levels alpha=.10, .05, .025 and .01. Normal and Edgeworth approximations for the significance probabilities are also given. A simplified version of the normal score test is proposed and its rejection regions are tabulated. These tests are compared with the correlation coefficient test, Kendall's t test and Spearman's rank correlation test for independence by means of Monte Carlo evaluation of power employing 10,000 trials from each of three different types of bivariate distributions. Also included is a brief description of the computing aspects of the problem that may prove useful in similar studies.
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