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How accurate is the Pearson r-from-Z approximation? A Monte Carlo simulation study
1a College of Charleston.
The Journal of General Psychology
|May 20, 2014
Summary
The Pearson r-from-Z approximation can estimate correlation from Z-scores, but its accuracy varies. This method is unreliable for small sample sizes and small effect sizes, requiring careful consideration for meta-analysis.
Area of Science:
- Statistics
- Psychometrics
- Meta-analysis
Background:
- The Pearson r-from-Z approximation offers a method to estimate sample correlation (effect size) using Z-scores and sample size.
- This approximation is particularly useful in meta-analysis when primary studies report limited statistical data.
Purpose of the Study:
- To empirically evaluate the accuracy of the Pearson r-from-Z approximation.
- To identify conditions under which this approximation yields valid inferences.
Main Methods:
- Monte Carlo simulations were conducted to assess the performance of the Pearson r-from-Z approximation.
- Simulations varied sample sizes and effect sizes to test the formula's accuracy.
Main Results:
- The Pearson r-from-Z approximation demonstrated accuracy in some scenarios.
- However, significant inaccuracies were observed with very small sample sizes (N=10) and small to moderate effect sizes (d=0.1, 0.3).
Conclusions:
- The Pearson r-from-Z approximation is not universally accurate and its reliability is contingent on sample size and effect size.
- Guidance is provided to help researchers determine the validity of using this approximation in their analyses.
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