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Correct standard errors can bias meta-analysis.

T D Stanley1, Hristos Doucouliagos1

  • 1Department of Economics, Deakin University, Burwood, Victoria, Australia.

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PubMed
Summary
This summary is machine-generated.

Researchers should avoid the "correct" standard error (SE) formula for partial correlation coefficients (PCC) in meta-analyses. Simulations reveal that an alternative SE formula leads to less biased random effects and statistically superior meta-analysis results.

Keywords:
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Area of Science:

  • Statistics
  • Psychometrics
  • Biostatistics

Background:

  • Partial correlation coefficients (PCC) are frequently employed as effect sizes in meta-analyses and systematic reviews of multiple regression research.
  • Two distinct formulas exist for calculating the variance and standard error (SE) of PCCs.

Purpose of the Study:

  • To evaluate the performance of two standard error formulas for partial correlation coefficients in meta-analytic contexts.
  • To determine which formula yields less biased results and statistically superior meta-analyses.

Main Methods:

  • The study utilized simulation methods to compare the two standard error formulas for partial correlation coefficients.
  • Simulations assessed the bias in random effects and the statistical dominance of meta-analyses generated using each formula.

Main Results:

  • The formula considered "correct" for PCC variance demonstrated increased bias in random effects compared to the alternative formula.
  • Meta-analyses employing the alternative SE formula statistically outperformed those using the "correct" SEs.
  • The alternative formula accurately reproduces test statistics and p-values from original multiple regression analyses.

Conclusions:

  • The "correct" formula for partial correlation coefficients' standard errors should not be used in meta-analysis.
  • The alternative variance formula is recommended for meta-analysts due to its superior performance and reduced bias.