Bootstrap Correlation Confidence Interval Estimation: The Positive Impact of a Symmetric Distribution

Abstract

Estimating confidence intervals (CIs) for the correlation has been a challenge because the correlation sampling distribution changes depending on the correlation magnitude. The Fisher z-transformation was one of the first attempts at estimating correlation CIs but has historically shown to not have acceptable coverage probability if data were non-normal. Bootstrap methods for correlation CIs were then proposed but have been met with mixed results. A recent study consolidating some of the previous literature found that the bootstrap correlation CIs had acceptable coverage probability for non-normal data if sample size was large enough. Additionally, it was found that pairing a normal distribution with any other distribution resulted in better coverage probability for all correlation CIs investigated. Notably, the Fisher z-transformation CI had consistent acceptable coverage probability in this case. Therefore, the purpose of the current study was to investigate if this normality effect extends to other distributions that are symmetric. It was found that the Fisher z-transformation, percentile bootstrap (PB), and bias-corrected and accelerated (BCa) CIs all benefited from having data that came from a symmetric distribution. However, the PB and BCa CIs did not have acceptable coverage probability when a uniform distribution was paired with a chi-square (df = 1).

Keywords:

• Confidence intervals
• correlation
• simulation

Disclosure statement

The authors have no conflicts of interest to disclose.