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Quantifying uncertainty in the meta-analytic lower bound estimate.
Michael T Brannick1, Sean Potter1, Yuejia Teng1
1Department of Psychology.
This study introduces new methods for calculating confidence intervals for the lower bound of credibility values in meta-analyses. Bootstrap confidence intervals for the lower bound (HOVr) are effective for correlations with sufficient studies.
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Area of Science:
- Statistics
- Psychometrics
- Research Methodology
Background:
- Meta-analyses typically report confidence intervals for mean effects, but not for the standard deviation or lower bound of credibility values.
- These unquantified values are crucial for interpreting meta-analysis results.
Purpose of the Study:
- To introduce and evaluate methods for computing confidence intervals for the lower bound of credibility values in meta-analyses.
- To compare the performance of Lawless and bootstrap methods with different lower bound estimators.
Main Methods:
- Introduced two methods: Lawless and bootstrap confidence intervals.
- Utilized three lower bound estimators: Schmidt-Hunter, Schmidt-Hunter with k correction, and Morris/Hedges (HOVr/HOVd).
- Conducted two Monte Carlo simulation studies for correlations and standardized mean differences.
Main Results:
- Bootstrap confidence intervals for HOVr provided over 90% coverage for correlations with at least 25 studies.
- For standardized mean differences, all three methods with bootstrap yielded acceptable results with >= 20 studies and average sample size >= 50.
- Small study numbers (k=8-10) resulted in <90% coverage and wide intervals. Indirect range restriction and small between-studies variance also negatively impacted coverage.
Conclusions:
- Bootstrap confidence intervals offer a viable solution for estimating the lower bound of credibility values in meta-analyses.
- The effectiveness of these methods is dependent on the number of studies, average sample size, and characteristics of the data.
- Software is provided to facilitate the computation of these bootstrap confidence intervals for meta-analysts.