Occasionally we need to compare paired data using mean differences (MD) as effect estimates for the purpose of a meta-analysis. In such cases, pooled SD can be approached by the formula [SDa2 + SDb2 – 2*r*SDa*SDb]½, where SDa, SDb and r denote SD of first group, SD of second group and correlation coefficient between data, respectively. In cases that r is unknown, can we use a reasonable arbitrary value? Some authors use 0.5; there is also Rosenthal’s approach of 0.7. What is your appoach?
Hello Vasileios,
If the studies in question have furnished both the means and SDs for each of the paired scores, then you can solve for the (unknown) value of r directly, given either a t-statistic or pooled SD.
If that information isn't given, you could try contacting the authors of the studies to ask for the values or access to the data so that you could compute them.
If neither of these is possible, you could pick an arbitrary value (such as the ones you mention). However, I'd suggest you choose multiple values, and run the meta-analysis multiple times, so that you could at least offer a suggestion as to: (a) how much/little difference the choice could make; and (b) how far off any one analysis might be from the true state of affairs.
Good luck with your work.
Thank you very much, @David Morse. In fact, I faced the third option you mentioned (I apologize for not being clear enough); your suggestion is very helpful.
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