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[R-meta] The P value of correlation coefficent in meta-analysis

Hi Pengzhen,

Oh dear, your intuition is obviously correct. If we exclude 
non-significant correlations, then we will overestimate the correlation. 
In other words, we would get a biased effect estimate.

This issue is addressed in many meta-analytic textbooks, e.g.
Borenstein, M., Hedges, L. V., Higgins, J. P., & Rothstein, H. R. 
(2021). Introduction to meta-analysis. John Wiley & Sons.

The authors offer a few free chapters, some of which could be useful in 
your case.
https://introduction-to-meta-analysis.com/download/c01.pdf
For example, Figure 1.1 (p. 4) clearly shows that studies with 
insignificant p-values are included in the meta-analysis.


The book also contains a chapter, "Vote counting - a new name for an old 
problem," which has a nice example showing that even when all individual 
studies have large p-values, the meta-analytic estimate can be 
statistically significant. By combining the individual studies, we 
increase the power and can detect even small effects.


Best,
Lukasz