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CONTEXT: We are to perform a meta-analysis of the difference between a and b. In all the collected studies, a and b are the mean times to failure in seconds of two different tasks performed by the same group. Is it correct to choose the path of "matched groups"? Referring to "Intro to meta-analysis" by Borenstein 2009, I (think) am supposed to calculate the standard deviation within groups (SDwithin) using the SD of the differences (SDdiff).

The formulas:

  • d = (a - b)/SDwithin
  • SDwithin = SDdiff/SQRT(2(1-r)); r is correlation index;
  • SDdiff = SQRT(a2+b2-2(r)(a)(b)).

THE PROBLEM: Since I am applying the above formulas to every study (e.g., for study n.1 => SDdiff = SQRT(a1^2+b1^2-2(r)(a1)(b1); for study n.2 =>SQRT(a2^2+b2^2-2(r)(a2)(b2) and so on) am I supposed to use the r of each study (i.e., r is the correlation between a and b of every subject within that study) or can I use the r calculated on means a and b, which is the same for all?

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  • $\begingroup$ If a and b represent the means then your last bullet point looks incorrect. $\endgroup$
    – mdewey
    Commented Aug 30 at 12:35
  • $\begingroup$ Thanks for you reply, @mdewey. Could you further explain in what terms SDdiff is incorrect? $\endgroup$
    – CrappyCoder
    Commented Aug 30 at 15:00
  • $\begingroup$ stats.stackexchange.com/questions/166308/… $\endgroup$
    – mdewey
    Commented Aug 30 at 15:32

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