Bootstrap Confidence Intervals for 11 Robust Correlations in the Presence of Outliers and Leverage Observations
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 circumstan...
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| Format: | Article |
| Language: | English |
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PsychOpen GOLD/ Leibniz Institute for Psychology
2022-06-01
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| Series: | Methodology |
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| Online Access: | https://meth.psychopen.eu/index.php/meth/article/view/8467 |
| _version_ | 1828074409916628992 |
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| author | Johnson Ching-Hong Li |
| author_facet | Johnson Ching-Hong Li |
| author_sort | Johnson Ching-Hong Li |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T01:43:11Z |
| format | Article |
| id | doaj.art-3d2b82e93cd54f27b6defee5fa95382f |
| institution | Directory Open Access Journal |
| issn | 1614-2241 |
| language | English |
| last_indexed | 2024-04-11T01:43:11Z |
| publishDate | 2022-06-01 |
| publisher | PsychOpen GOLD/ Leibniz Institute for Psychology |
| record_format | Article |
| series | Methodology |
| spelling | doaj.art-3d2b82e93cd54f27b6defee5fa95382f2023-01-03T08:14:08ZengPsychOpen GOLD/ Leibniz Institute for PsychologyMethodology1614-22412022-06-011829912510.5964/meth.8467meth.8467Bootstrap Confidence Intervals for 11 Robust Correlations in the Presence of Outliers and Leverage ObservationsJohnson Ching-Hong Li0Department of Psychology, University of Manitoba, Winnipeg, MB, CanadaResearchers 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.https://meth.psychopen.eu/index.php/meth/article/view/8467robust correlationbootstrap confidence intervalsoutliersmonte carlo simulation |
| spellingShingle | Johnson Ching-Hong Li Bootstrap Confidence Intervals for 11 Robust Correlations in the Presence of Outliers and Leverage Observations Methodology robust correlation bootstrap confidence intervals outliers monte carlo simulation |
| title | Bootstrap Confidence Intervals for 11 Robust Correlations in the Presence of Outliers and Leverage Observations |
| title_full | Bootstrap Confidence Intervals for 11 Robust Correlations in the Presence of Outliers and Leverage Observations |
| title_fullStr | Bootstrap Confidence Intervals for 11 Robust Correlations in the Presence of Outliers and Leverage Observations |
| title_full_unstemmed | Bootstrap Confidence Intervals for 11 Robust Correlations in the Presence of Outliers and Leverage Observations |
| title_short | Bootstrap Confidence Intervals for 11 Robust Correlations in the Presence of Outliers and Leverage Observations |
| title_sort | bootstrap confidence intervals for 11 robust correlations in the presence of outliers and leverage observations |
| topic | robust correlation bootstrap confidence intervals outliers monte carlo simulation |
| url | https://meth.psychopen.eu/index.php/meth/article/view/8467 |
| work_keys_str_mv | AT johnsonchinghongli bootstrapconfidenceintervalsfor11robustcorrelationsinthepresenceofoutliersandleverageobservations |