7: Fixed & Random Summaries in r and d with Preferred Input Fixed and random-effects overall or summary effects for correlations and mean differences Meta-analysis in R with Metafor

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, doi: /a 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