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