Correct standard errors can bias meta-analysis

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.