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

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Sun May 23 19:06:01 CEST 2021

```Dear Dakis,

All three methods you listed should give you identical results.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Dakis-Yaoba OUEDRAOGO
>Sent: Tuesday, 18 May, 2021 17:00
>To: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] Which method to compute 95% confidence intervals around
>individual effect sizes (standardized mean differences) ?
>
>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

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