Meta-analyses of partial correlations are biased: Detection and solutions

Area of Science:

• Statistics
• Quantitative Research Methods

Background:

• Meta-analyses of partial correlation coefficients (PCCs) are widely used across various scientific disciplines.
• Existing meta-analysis methods for PCCs are subject to bias, particularly in small sample sizes (n < 200).

Approach:

• Introduction of a novel statistical method, UWLS+3 (unrestricted weighted least squares weighted average).
• UWLS+3 adjusts the degrees of freedom for partial correlations to minimize meta-analysis bias.
• A simple correction factor, (n-2)/(n-1), is proposed to reduce small-sample biases when combined with Fisher's z transformation.

Key Points:

• All meta-analyses of partial correlations exhibit bias.
• Small-sample biases are a significant issue in fields with limited data.
• The proposed UWLS+3 method and correction factor effectively mitigate these biases.

Conclusions:

• Standard meta-analysis methods for partial correlations yield negligible bias with large sample sizes (n > 200).
• The UWLS+3 method provides a robust solution for meta-analyzing partial correlations in small-sample research.
• Adoption of these methods will improve the accuracy and reliability of meta-analytic findings in social and medical sciences.