I am following recommendations in Borenstein et al. (2009) who provides formulas to convert log odds ratio to d and d to r. For the last step (d to r), you are supposed to use a correction factor when n1#n2. While I generally understand why this is necessary when transforming d to r, what are the implications when your starting point has been an OddsRatio based on two dichotomous variables and n1#n2 is the case for both of them? Would I choose the sample size ratio of one variable then (e.g., the more extreme one, to err on the side of caution)?
Borenstein, M., Hedges, L. V., Higgins, J. P., & Rothstein, H. R. (2011). Introduction to meta-analysis. John Wiley & Sons.
I guess that one solution might be to convert to r based on information from the contingency table (instead of the odds ratio) but in many cases, this is not provided.
On a side note, if I use the correction factor here, would I also need to correct point-biserial correlations when n1#n2? Or is this a completely unrelated issue?
As Borenstein et al. state in their textbook, you can inter-convert effect sizes but the question is "should you". Because you want to convert your effect sizes to Pearson correlations, that means to me you are interested in the relationship of two continuous variables. How would a study using an odds ratio, which looks at the relationship between two dichotomous variables, answer your question about the relationship of two continuous variables? Should you be including studies with odds ratios in your systematic review/meta-analysis? Does the study meet all of your study eligibility criteria?
Thanks for your thoughtful reply.
In this particular case, I think that it is warranted to transform Odds ratios to r. I consider evidence from different disciplines with different reporting standards. That means that in some cases, variables that had been assessed at a metric or ordinal level have been artificially dichotomized (but note that most authors report Pearson r). If I leave studies like this out it could also lead to bias. So I am trying to find the best way to deal with this situation.
I believe Borenstein demonstrates calc of conversion factor in Excel. That said, maybe an online converter has the paramters designed to input correction factors?
Hope this helps
Matt
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