Colleagues,
I am conducting a meta-analysis and our effect size metric is r. I would like to hear your opinions on including standardized regression beta weights as a substitute for r when r is not reported. My basic understanding from reading Peterson and Brown (2005; article attached) is that both beta and r are highly correlated, the relationship is not substantially affected by the number of predictors in the model, and thus beta can be substituted for r. Further research into this issue have led me to conclude that opinion is divided - some researchers are in favor of it, others advise against its inclusion. I have found some recent meta-analysis that have included betas in their analyses using the formulas recommended by Peterson & Brown.
I would greatly appreciate your insights.
Dear Donaldo,
I think the peterson and Brown's work is a classic one. See also the attached paper.
You may consider using the regression coefficients in your analysis, and then performing a post-hoc sensitivity analysis to check the possible influence of those studies on the overall estimate.
Hope this helps,
Gianluca
I am in favour of including standardized regression coefficients in meta-analysis if the correlation coefficients are not reported. As suggested earlier, do a sensitivity analysis to find out possible influence on your overall estimate.
Do not do this. They are not equivalent unless they are uncorrelated. If you have the pxp correlation matrix of predictors, Rxx, along with the px1 vector of standardized betas B, then the p x 1 vector of validities Rxy for meta-analysis is = Rxx*B.
Betas and r are different metrics, and, under normal conditions, the betas will be smaller than the rs (i.e., correlated without supression effects). If you are doing some form of null hypothesis testing and want to be superconservative, you could include betas. If you are interested in estimating an overall effect size, then only use rs.
Is it also possible to use the formula by Peterson & Brown (2005) for logistic regression?
Nicola : I think it is, but be careful. As I remember, the betas need to be between -0.5 and 0.5 (check the article for real values). In my field, this was impossible to achieve.
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