Bootstrap confidence intervals for 11 robust correlations in the presence of outliers and leverage observations

Abstract

Researchers often examine whether two continuous variables (X and Y) are linearly related. Pearson’s correlation (r) is a widely-employed statistic for assessing bivariate linearity. However, the accuracy of r is known to decrease when data contain outliers and/or leverage observations, a circumstance common in behavioral and social sciences research. This study compares 11 robust correlations with r and evaluates the associated bootstrap confidence intervals [bootstrap standard interval (BSI), bootstrap percentile interval (BPI), and bootstrap bias-corrected-and-accelerated interval (BCaI)] across conditions with and without outliers and/or leverage observations. The simulation results showed that the median-absolute-deviation correlation (r-MAD), median-based correlation (r-MED), and trimmed correlation (r-TRIM) consistently outperformed the other estimates, including r, when data contain outliers and/or leverage observations. This study provides an easy-to-use R code for computing robust correlations and their associated confidence intervals, offers recommendations for their reporting, and discusses implications of the findings for future research.