Correct standard errors can bias meta‐analysis

• Published in: Research synthesis methods Vol. 14; no. 3; pp. 515 - 519
• Main Authors: Stanley, T. D., Doucouliagos, Hristos
• Format: Journal Article
• Language: English
• Published: England Wiley 01.05.2023; Wiley Subscription Services, Inc
• Subjects: Bias; Coefficient of variation; Correlation; Correlation coefficients; Effect Size; Error Correction; Error Patterns; Mathematical Formulas; mean square errors; Meta Analysis; Meta-Analysis as Topic; Multiple regression analysis; partial correlation coefficients; Regression (Statistics); Regression coefficients; Sampling; Standard error; Standard error of estimate; Statistical Bias; Statistical Distributions; Statistical tests; Variance analysis; meta-analysis; partial correlation coefficients; bias; mean square errors
• ISSN: 1759-2879; 1759-2887
• DOI: 10.1002/jrsm.1631

Partial correlation coefficients are often used as effect sizes in the meta‐analysis and systematic review of multiple regression analysis research results. There are two well‐known formulas for the variance and thereby for the standard error (SE) of partial correlation coefficients (PCC). One is considered the “correct” variance in the sense that it better reflects the variation of the sampling distribution of partial correlation coefficients. The second is used to test whether the population PCC is zero, and it reproduces the test statistics and the p‐values of the original multiple regression coefficient that PCC is meant to represent. Simulations show that the “correct” PCC variance causes random effects to be more biased than the alternative variance formula. Meta‐analyses produced by this alternative formula statistically dominate those that use “correct” SEs. Meta‐analysts should never use the “correct” formula for partial correlations' standard errors.