Hi all, I am kind of struggling with calculation of the harmonic mean for applying SEM on meta-analytic correlations.
Let's say I have a 3x3 matrix with variables A, B and C.
Number of samples and corresponding Ns are:
A-B: k = 15, N = 1000
A-C: k = 8, N = 450
B-C: k =3, N = 300
How would I calculate the harmonic mean of the total correlation matrix? I guess it would be 3/(1/1000+1/450+1/300) = 458. Is this the correct way?
Hope you can help! Regards, Dirk
Sorry, I don't get what you mean, and by the lack of answers here, maybe nobody else does either. If it helps, wikipedia nicely describes the harmonic mean as the reciprocal of the arithmetic mean of the reciprocals, which is what you've done. But to be honest, I've never used it and can't immediately see why you'd want to, or why you need to combine these different correlations. I don't know if this helps you at all, at least to rephrase your question?
Your calculation is correct. You can input the matrix of the sample sizes into an Excel file and then directly use the formula of harmonic mean (HARMEAN) to get the result.
The harmonic mean is calculated by k/(1/N1 +1/N2+…+1/Nk), where k equals the number of meta-analytic correlations, and N1…Nk
refer to each of the total sample sizes used to compute each of the meta-analytically derived correlations (Brown et al., 2008).
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