Estimating confidence intervals (CIs) for the correlation has been a challenge. The challenge stems from the metamorphic nature of the sampling distribution of the correlation being bound by-1≤ρ≤1. The nonparametric nature of the bootstrap makes it a good option for estimating correlation CIs. However, there have been mixed results about the robustness of bootstrap CIs for the correlation with non normal data. This had led the literature to suggesting the use of transformation methods to estimate correlation CIs. However, transformation methods carry a risk of the original data being misrepresented. Thus, further investigation of bootstrap CIs for the correlation is necessary to provide pertinent information in choosing a correlation CI.
Here, the coverage probability of non bootstrap and bootstrap CIs for the correlation are investigated. This was done with a simulation that has condition parity with previous research yet expands upon these conditions. The non bootstrap CIs investigated were the Fisher z transformation, Spearman rank order, and ranked inverse normal (RIN) Transformation. The bootstrap CIs investigated were the percentile bootstrap (PB), bias corrected and accelerated bootstrap (BCa), and highest probability density interval (HPDI). All CIs were assessed for 95% coverage probability and the corresponding correlation estimates were assessed with standardized bias. The PB and BCa CIs were the focus of the study and were found to have good coverage probability overall.
","abstract_html":"<p>Estimating confidence intervals (CIs) for the correlation has been a challenge. The challenge stems from the metamorphic nature of the sampling distribution of the correlation being bound by-1≤ρ≤1. The nonparametric nature of the bootstrap makes it a good option for estimating correlation CIs. However, there have been mixed results about the robustness of bootstrap CIs for the correlation with non normal data. This had led the literature to suggesting the use of transformation methods to estimate correlation CIs. However, transformation methods carry a risk of the original data being misrepresented. Thus, further investigation of bootstrap CIs for the correlation is necessary to provide pertinent information in choosing a correlation CI.</p> <p>Here, the coverage probability of non bootstrap and bootstrap CIs for the correlation are investigated. This was done with a simulation that has condition parity with previous research yet expands upon these conditions. The non bootstrap CIs investigated were the Fisher z transformation, Spearman rank order, and ranked inverse normal (RIN) Transformation. The bootstrap CIs investigated were the percentile bootstrap (PB), bias corrected and accelerated bootstrap (BCa), and highest probability density interval (HPDI). All CIs were assessed for 95% coverage probability and the corresponding correlation estimates were assessed with standardized bias. The PB and BCa CIs were the focus of the study and were found to have good coverage probability overall.</p>","abstract_has_math":false,"creators":["DelosReyes, John Mart V."],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Thesis","degree_discipline":"Psychology","degree_department":null,"school":null,"contributors":["Miguel A. Padilla","James H. Henson","Jing Chen"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-10-01T07:00:00Z","date_published":"2019-10-01T07:00:00Z","updated_at":"2026-07-24T03:35:30Z","subjects":["Bootstrap","Confidence interval","Correlation","Fisher Z","Non-normal","Robust","Quantitative Psychology"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
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Here, the coverage probability of non bootstrap and bootstrap CIs for the correlation are investigated. This was done with a simulation that has condition parity with previous research yet expands upon these conditions. The non bootstrap CIs investigated were the Fisher z transformation, Spearman rank order, and ranked inverse normal (RIN) Transformation. The bootstrap CIs investigated were the percentile bootstrap (PB), bias corrected and accelerated bootstrap (BCa), and highest probability density interval (HPDI). All CIs were assessed for 95% coverage probability and the corresponding correlation estimates were assessed with standardized bias. The PB and BCa CIs were the focus of the study and were found to have good coverage probability overall.
"]},{"key":"dc:title","label":"Title","values":["Estimation of Correlation Confidence Intervals via the Bootstrap: Non-Normal Distributions"]}]}],"canonical_facts":{"dc:contributor":["Miguel A. Padilla","James H. Henson","Jing Chen"],"dc:creator":["DelosReyes, John Mart V."],"dc:date.available":["2020-02-03T08:00:00Z"],"dc:description.abstract":["Estimating confidence intervals (CIs) for the correlation has been a challenge. The challenge stems from the metamorphic nature of the sampling distribution of the correlation being bound by-1≤ρ≤1. The nonparametric nature of the bootstrap makes it a good option for estimating correlation CIs. However, there have been mixed results about the robustness of bootstrap CIs for the correlation with non normal data. This had led the literature to suggesting the use of transformation methods to estimate correlation CIs. However, transformation methods carry a risk of the original data being misrepresented. Thus, further investigation of bootstrap CIs for the correlation is necessary to provide pertinent information in choosing a correlation CI.
Here, the coverage probability of non bootstrap and bootstrap CIs for the correlation are investigated. This was done with a simulation that has condition parity with previous research yet expands upon these conditions. The non bootstrap CIs investigated were the Fisher z transformation, Spearman rank order, and ranked inverse normal (RIN) Transformation. The bootstrap CIs investigated were the percentile bootstrap (PB), bias corrected and accelerated bootstrap (BCa), and highest probability density interval (HPDI). All CIs were assessed for 95% coverage probability and the corresponding correlation estimates were assessed with standardized bias. The PB and BCa CIs were the focus of the study and were found to have good coverage probability overall.
"],"dc:identifier":["9781392539521","https://digitalcommons.odu.edu/psychology_etds/336"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Bootstrap","Confidence interval","Correlation","Fisher Z","Non-normal","Robust","Quantitative Psychology"],"dc:title":["Estimation of Correlation Confidence Intervals via the Bootstrap: Non-Normal Distributions"],"thesis:degree_discipline":["Psychology"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T03:35:30Z"}