Bootstrap Confidence Intervals for 11 Robust Correlations in the Presence of Outliers and Leverage Observations


  • Johnson Ching-Hong Li


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.