[R-meta] Correcting gain effects in nested studies

[Zhouhan Jin]

Hello All,

Hedges (2007) provides formulas for adjusting SMD effects (g) and their SEs for when primary studies have a nested design (below).

But I want to compute gain effects (ex. SMCC in metafor::escalc) from my nested studies, not SMDs.

So, how can I adjust my SMCCs and their SEs for nestedness in the primary studies?


adjusted_g =  g * sqrt(1 - ((2 * (n_bar - 1) * icc) /
                  (n_cluster * n_bar - 2)))

adjusted_SE =  ((Nt+Nc)/(Nt*Nc))*(1 + ((n_bar- 1)*icc)) +
    ( g^2 * (
      (((N_tot -2)*(1-icc)^2 ) + (n_bar*(N_tot - 2*n_bar)*icc^2) +
         (2* (N_tot - 2*n_bar) * icc * (1 - icc)) ) /
        ((2* (N_tot-2)) * ( (N_tot-2) - (2* (n_bar-1)*icc) ))
    )  )

Thanks a lot!

Best wishes,

Zhouhan


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