Bootstrapping to test for nonzero population correlation coefficients using univariate sampling.

This article proposes 2 new approaches to test a nonzero population correlation (rho): the hypothesis-imposed univariate sampling bootstrap (HI) and the observed-imposed univariate sampling bootstrap (OI). The authors simulated correlated populations with various combinations of normal and skewed variates. With alpha set=.05, N> or =10, and rho< or =0.4, empirical Type I error rates of the parametric r and the conventional bivariate sampling bootstrap reached .168 and .081, respectively, whereas the largest error rates of the HI and the OI were .079 and .062. On the basis of these results, the authors suggest that the OI is preferable in alpha control to parametric approaches if the researcher believes the population is nonnormal and wishes to test for nonzero rhos of moderate size.