Meta-analysis in R with Metafor
7: Fixed & Random Summaries in r
and d with Preferred Input
Fixed and random-effects overall or summary effects for correlations and
mean differences
Overall Summary
The Metafor program uses inverse variance weights to combine study ES
into an overall or summary effect size
You can specify Fixed (common) effects analysis or Random (varying) effects
analysis
If RE, you can choose from several methods for estimating the random effects
variance component (REVC). Different REVC, weight, summary.
The method statement specifies both fixed or random and which REVC
estimator you want
The effect sizes input to metafor may be transformed in various ways
The measure option tells metafor what transformation you want
Correlation Measures
If you input r and N, you can choose either the raw correlations or one of
two transformations for the analysis using measure = “choice” command :
“COR” – Pearson correlation and associated variance
Vtype = “LS” is the default. The large sample approximation is used for the
variance.
Vtype = “UB” provides and unbiased estimate of the sampling variance.
“UCOR” – correction for slight bias in Pearson correlation
Vtype = “LS” is the default. The large sample approximation is used for the
variance.
Vtype = “UB” provides and unbiased estimate of the sampling variance.
“ZCOR” Fisher’s z transformation and associated variance
R code: LMX & AC
Rockstuhl, T., Dulebohn, J. H., Ang, S., & Shore, L. M. (2012). Leader–member
exchange (LMX) and culture: A meta-analysis of correlates of LMX across 23
countries. Journal of Applied Psychology, 97, 1097-1130. doi:10.1037/a0029978
Measure=“COR” and method =“HS”
Note that choosing the Hunter-Schmidt estimator, Metafor still uses the inverse
variance method, and does not produce the same analysis as would following the
method in Hunter and Schmidt’s 2004 book.
Measure =“ZCOR” and method=“DL”
Note that analysis is in Z and is not transformed back to r. You must do that, and the
variance cannot be transformed directly, but the confidence and credibility limits can.
Show R code and results
Mean Differences
If you use the preferred format (M, SD, N for each group), you can choose
measure = “choice” :
“MD” mean difference (no standardizing for pooled SD)
This is not usually feasible because you need exactly the same measurement or
scale across all the studies (e.g., if every study compared men to women on the
Beck Depression Index)
“SMD” for standardized mean difference
The usual choice (e.g., all studies compared men and women on depression, but
they used different scales to measure depression)
R code:
Appetite study – manufactured data
Measure=“MD”, method = “DL”
Measure=“SMD”, method=“DL”
Measure=“SMD”, method=“REML”
Show R code and results