# [R-meta] Which method to compute 95% confidence intervals around individual effect sizes (standardized mean differences) ?

Dakis-Yaoba OUEDRAOGO d@k|@-y@ob@@ouedr@ogo @end|ng |rom mnhn@|r
Tue May 18 16:59:53 CEST 2021

```Dear all,

I am gathering studies about effects of various chemicals on corals, and for every concentration of a chemical I computed the standardized mean differences for several outcomes. My final goal is to know for which maximal concentration of a chemical no significant effect is observed, and for which minimal concentration of a chemical a significant effect is observed.
To get this I computed the 95% confidence intervals around the standardized mean differences to identify the effect sizes that are significantly/non significantly different from zero.

I am quite confused about how to properly compute these condidence intervals. I could see 3 different types of CI :

1/ 95% CI assuming a normal distribution
data\$cilow <- data\$yi - sqrt(data\$vi)*qnorm(0.05/2, lower.tail = FALSE)
data\$ciup <- data\$yi + sqrt(data\$vi)*qnorm(0.05/2, lower.tail = FALSE)

2/ 95% Wald-type confidence intervals
These are computed using the summary.escalc() function in metafor

3/ The confidence intervals computed from a multi-level model rma.mv where a variance-covariance matrix V is specified to take into account that I have several concentrations compared to the same control (Correction of Gleser & Olkin, I followed the tutorial in
http://www.metafor-project.org/doku.php/analyses:gleser2009#quantitative_response_variable
to compute V)

mod <- rma.mv(yi=yi, V=V, mods= ~1, random= ~1 | ID_case, data=data, method="REML")

With forest(mod) I can see the individual study 95%CI on the plot and I can get them with
mod\$yi - sqrt(mod\$vi)*qnorm(0.05/2, lower.tail = FALSE)
mod\$yi + sqrt(mod\$vi)*qnorm(0.05/2, lower.tail = FALSE)

Because the method chosen to compute the 95% CI around the individual standardized mean differences will greatly influence the conclusions about the problematic chemical concentrations, I will greatly appreciate any help, comment or advise on my issue.

Best wishes,
Dakis

```