[R-meta] Back-transforming Fisher's r-to-z transformed correlation coefficient to r in funnel and forest plots results

CAUTION: Email Originated Outside of Auburn.

Hi All,

I performed a random-effect summary meta-analysis where study was used as a random effect. Here, I used the rma.mv function using the Fisher's r-to-z transformed correlation coefficient effect size (see code below).

CODE: results=rma.mv(yi,vi,data=datum,method="REML",random=~1|Study)

I can use then use the below code to create funnel and forest plots.

CODE: forest(results)
CODE: funnel(results)

The x axis for these plots would be my effect size (Fisher's r-to-z transformed correlation coefficient). My question is, what must I do in order to back transform my Fisher's r-to-z transformed correlation coefficient here in the plots so that they are displayed as the Pearson's correlation coefficient (r).

Thanks,

John

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CAUTION: Email Originated Outside of Auburn.

Dear John,

That would be one way of doing this, but then your analysis uses raw correlation coefficients. The forest() and funnel() functions have the 'atransf' arguments for back-transforming the x-axes.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On
>Behalf Of John Mahas via R-sig-meta-analysis
>Sent: Wednesday, 16 August, 2023 22:05
>To: R Special Interest Group for Meta-Analysis
>Cc: John Mahas
>Subject: Re: [R-meta] Back-transforming Fisher's r-to-z transformed correlation
>coefficient to r in funnel and forest plots results
>
>Hi All,
>
>Please disregard my previous message - I figured it out. I isolated my generated
>yi and vi from my dataset and ran the following code.
>
>#load z results
>datum=read.csv(file.choose())
>Z=datum
>
>#transform z to r
>Z_r=transf.ztor(Z)
>
>Once this was done, I added this data to a csv to perform my analyses with the
>back-transformed r instead of my original Fisher's r-to-z transformed correlation
>coefficient
>
>________________________________
>From: R-sig-meta-analysis <r-sig-meta-analysis-bounces at r-project.org> on behalf
>of John Mahas via R-sig-meta-analysis <r-sig-meta-analysis at r-project.org>
>Sent: Wednesday, August 16, 2023 2:36 PM
>To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-
>project.org>
>Cc: John Mahas <jwm0055 at auburn.edu>
>Subject: [EXT] [R-meta] Back-transforming Fisher's r-to-z transformed correlation
>coefficient to r in funnel and forest plots results
>
>Hi All,
>
>I performed a random-effect summary meta-analysis where study was used as a
>random effect. Here, I used the rma.mv function using the Fisher's r-to-z
>transformed correlation coefficient effect size (see code below).
>
>CODE: results=rma.mv(yi,vi,data=datum,method="REML",random=~1|Study)
>
>I can use then use the below code to create funnel and forest plots.
>
>CODE: forest(results)
>CODE: funnel(results)
>
>The x axis for these plots would be my effect size (Fisher's r-to-z transformed
>correlation coefficient). My question is, what must I do in order to back
>transform my Fisher's r-to-z transformed correlation coefficient here in the
>plots so that they are displayed as the Pearson's correlation coefficient (r).
>
>Thanks,
>
>John