Standard and bootstrap confidence intervals for the correlation coefficient

Abstract

Several articles in the field of psychology have shown simulation results with the bootstrap‐percentile method and variants for the (Pearson) correlation coefficient. The overall result was that with non‐normal (especially skewed) data, ρ ≠ 0 and small and medium sample sizes, bootstrap methods show poor coverage accuracy. Some of the authors call into question the ability of any bootstrap methods of valid confidence intervals or acceptance regions for testing hypotheses about ρ under these conditions. Simulation results with the iterated bootstrap will be shown, which clearly demonstrate the ability of this bootstrap method to induce valid confidence intervals under all of the above mentioned conditions not only for ρ, but also for the difference of two correlation coefficients and the squared correlation coefficient. Simulations with the point‐biserial correlation coefficient show that for ρph ≠ 0, valid confidence intervals can be achieved with the iterated bootstrap only with medium or large sample sizes, depending on the distribution, while the standard method fails even then.