Bootstrap confidence intervals for 11 robust correlations in the presence of outliers and leverage observations
Bibliographic record
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.055 | 0.389 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".