Empirical Size, Coverage, and Power of Confidence Intervals for Spearman's Rho

Abstract

Several methods of constructing confidence intervals (CIs) for Spearman's rho were tested in a Monte Carlo investigation. A total of 2,000 samples of sizes 10, 50, and 200 were randomly drawn from bivariate normal populations with p, equal to .00, .29, .43, .58, .73, and .89. Each method for computing a 95% CI around p3 was evaluated with regard to size in the null case and power and coverage in non-null cases. Fisher's z transformation of r, worked well provided N was not small and Ps was not too large. The CIs constructed using the variance estimate for product-moment correlations had coverages that were consistently too liberal. Kraemer's method for establishing CIs produced coverages that were conservative. An empirical attempt to adjust the Fisher CI maintained Type I error rate near the nominal level in all cases with no loss of power. Arguments are made for the continued use of r, in behavioral research.