How to transform

[Matt Savage]

Hi all,

I'm currently completing a meta-analysis on 3 studies that report Pearson's correlations.

I've done a lot of reading around and the best way of doing this is doing Fishers-z transformation to perform the meta-analysis. I have done this with the code posted below. My understanding is that the forestplot this generates is therefore plotting the z values, and i need to convert them back to Pearson's r. How can I go about doing this?

Thanks in advance for help!
Best wishes,
Matt

---

**PFJ meta // PATELLA
clear
. input str12(study year time biomech outcome) float(r n)
"W**" "2023" "3 months" "contact force" "T2 relaxation time" -0.089 30
"L*" "2023" "6 months" "contact force" "T2 relaxation time" -0.49 49
"S**" "2023" "1 year" " contact force" "MRI MOAKS score" -0.1459 32
end

label variable year "{bf:Year}"
label variable time "{bf:Time}"
label variable biomech "{bf:Biomech}"
label variable outcome "{bf:Outcome}"
label variable r "{bf:Effect size}"
label variable n "{bf:Sample} {bf:size}"
format study time biomech %-12s

gen fisher_z = atanh(r)
generate sez = sqrt(1/(n-3))

metan fisher_z sez, effect("{bf:Effect size}") labtitle("{bf:Author}") lcols(year time outcome n) astext(60) xlabel(-1 "-1 (Deterioration)" 0 "No change" 1 "+1 (Improvement)") label(namevar = study) random
display _newline ///
"Pooled estimate of r = " tanh(r(ES)) _newline ///
"Lower limit of 95% CI = " tanh(r(ci_low)) _newline ///
"Upper limit of 95% CI = " tanh(r(ci_upp))