[R-meta] Formula SD in metafor package

[Emmelie Simoens]

Dear all,

We are doing a meta-analysis for a paired data design. Our effect size is a bit awkward because we are ultimately interested in a standardized paired mean difference of a standardized paired mean difference. To do this we will use the escalc function with the SMCC measure. Our function will be looking like this:

escalc(measure = �SMCC�,
      m1i = meandifference1 � meandifference2,
      m2i = meandifference3 � meandifference4,
      sd1i = sqrt(SD1^2 + SD2^2 -
                  2*CorrelationMean12*SD1*SD2),
      sd2i = sqrt(SD3^2 + SD4^2 -
                  2* CorrelationMean34*SD3*SD4),
      ni  = Samplesize ,
      ri  = 0.3, #this will be a hypothesized measure
      data = Data)

Now, our question is what formula uses the metafor package for calculating the pooled SD?
Does it use the same formula as us:  sqrt (SD1^2 + SD2^2 � 2 * r * SD1 * SD2) or the following SD-within formula: sqrt ( ( n1-1)*S^21 + (n2-1)*S^22 )/(n1 + n2 -2)?  We just want to make sure that our inserted formulas are in line with the underlying computation.

Many thanks,
Emmelie

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