Bootstrapped Deattenuated Correlation: Nonnormal Distributions

Correlation attenuation due to measurement error and a corresponding correction, the deattenuated correlation, have been known for over a century. Nevertheless, the deattenuated correlation remains underutilized. A few studies in recent years have investigated factors affecting the deattenuated correlation, and a couple of them provide alternative solutions based on the deattenuated correlation. One study proposed bootstrap confidence intervals (CIs) for the deattenuated correlation. However, CI research for the deattenuated correlation is in the beginning phases. Therefore, the bootstrapped deattenuated correlation CIs are investigated for 95% coverage through a Monte Carlo simulation that includes nonnormal distributions. Overall, both the bias-corrected and accelerated (BCa) and percentile bootstrap (PB) CIs had good performance, but the BCa CIs had slightly better coverage. In addition, with the exception of the Pareto distribution, both CIs had good coverage under all simulation conditions and across all other investigated distributions (i.e., the Normal, Uniform, Triangular, Beta, and Laplace).