Bootstrap confidence intervals for the mean correlation corrected for Case IV range restriction: a more adequate...

Area of Science:

• Psychometrics
• Statistical Methods
• Organizational Psychology

Background:

• Meta-analysis often involves correcting correlation coefficients for range restriction.
• Accurate confidence intervals are crucial for interpreting corrected correlations in meta-analytic research.
• Existing methods for confidence intervals of corrected correlations may lack precision.

Purpose of the Study:

• To propose and evaluate the nonparametric bootstrap procedure for constructing confidence intervals for mean correlation corrected for Case IV range restriction.
• To compare the accuracy of parametric and various nonparametric bootstrap confidence intervals.
• To assess the performance of the mean-corrected correlation estimate.

Main Methods:

• A comprehensive Monte Carlo simulation study was conducted.
• Parametric confidence intervals and three types of nonparametric bootstrap confidence intervals (including BCaI) were evaluated.
• The accuracy of the mean-corrected correlation (r(c4)) was compared to the uncorrected estimate.

Main Results:

• The bootstrap bias-corrected and accelerated percentile interval (BCaI) demonstrated the highest accuracy across various data conditions.
• The mean-corrected correlation (r(c4)) provided a more accurate estimate than the uncorrected correlation.
• BCaI outperformed other intervals in precision and coverage.

Conclusions:

• The nonparametric bootstrap BCaI is recommended for constructing confidence intervals for mean correlation corrected for Case IV range restriction in meta-analysis.
• The mean-corrected correlation estimate offers improved accuracy in meta-analytic research.
• These findings have significant implications for statistical practices in organizational studies.