[R-meta] question on scatter plot of estimates (Fisher's Z) against the standard error

[Gabriel Cotlier]

Hello all,
I have found that when I do the square root of the variance in the y axis
and the Fisher's z estimates in the x axis instead of following the formula
for the standard error (SE =  sd (x) / sqrt (length (x)), I do get the same
scatter of points as in the funnel plot, but the scale in y axis is
different from that in the funnel plot.
I possible to receive an explanation of why, using the square root of the
variance, I obtain the same distribution of points as in the funnel figure?
I would also like to have in the scatter plot the same scale of values as
in the funnel plot which is different if I use the square root of the
variance, How could this be possible?
Thanks a lot for your help and guidance.
Kind regards.
Gabriel.



On Tue, Jul 18, 2023 at 9:37 AM Gabriel Cotlier <gabiklm01 using gmail.com> wrote:

> Hello all,
>
> I would like to show in a scatter plot the relationship existing between
> the estimates (Fisher's z correlation) and a given measure of
> uncertainty (e.g., standard error) as is in the funnel plot. My intention
> is to obtain the funnel plot as in the function metafor::funnel ()
> suppressing all the funnel distribution background and keeping only the
> scatter plot. With the aim of having a graph of the relationship between
> the data and an uncertainty measure in the data, and if it is also
> possible, a numerical measure of uncertainty in addition to the scatter
> plot graph. Is this possible?
>
> However, when I tried to calculate the standard error by myself, I did not
> get the same result as in the output of the metafor::funnel() function
> without the funnel distribution background I wanted to suppress.
>
> ## CODE
> ## the model output is saved in the variable named "funnel_all"
> ## Estimates Fisher's Z extracted from general model
> yi_data <-funnel_all$yi[1:150]
>
> ## calculate standard error SE (formula =
> sd(estimtes_fisher_z)/sqrt(N_estimtes))
>
> ## 1. Directly with the data:
> N = 150 # number of samples
> SE <- 1/(sd(yi_data)/sqrt(N))
>
> ## 2. using a function:
> std <- function(x) sd(x)/sqrt(length(x))
> SE <- std(yi_data)
>
> Then, in the obtained plot of the estimates (Fisher's z ) against the SE,
> the results do not match the same output of the function mertafor::funnel()
> but without the funnel distribution in the background of the plot.
>
> How could this be possible to achieve?
> Thanks a lot for your guidance and help.
> Kind regards,
> Gabriel
>
>
>
>

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