# [R-meta] Question about my Effect Size Calculation

Sera Wiechert @@w|echert @end|ng |rom uv@@n|
Mon May 17 11:32:24 CEST 2021

```Dear R-sig-meta-analysis Community,

Currently, I am in the process of conducting my own meta-analysis. For this, I need to use a slightly awkward effect size measure, namely a standardized difference of a standardized difference.

To clarify a bit further - in the paradigm that I am investigating, they are comparing means between two groups of list conditions (critical vs unrelated). And I am additionally interested in the effect of negative valence (in comparison to neutral valence). So, I am looking at: neutral condition (critical mean - unrelated mean) - negative condition (critical mean- unrelated mean). For this, I tried to use the metafor package (for matched/paired designs).

As I am using the effect size calculation twice to get to my "end" effect size, I am unsure on how to convert the variance output of the first effect size calculation into a SD to be able to use it again in the second calculation.

I have now done it as follows:

library(metafor)
Data\$Correlationwithin <- rep(0.7, nrow(Data))
Data\$Correlationbetweenemotion <- rep(0.6, nrow(Data))

Neutral <- escalc(measure = "SMCC", m1i = Data\$NeutralCritical, m2i = Data\$NeutralUnrelated,
sd1i = Data\$NeutralCriticalSD, sd2i = Data\$NeutralUnrelatedSD, ni= Data\$`Number PP`, ri = Data\$Correlationwithin)

##calculate effect sizes for negative: critical-unrelated
Negative <- escalc(measure = "SMCC", m1i = Data\$NegativeCritical, m2i = Data\$NegativeUnrelated,
sd1i = Data\$NegativeCriticalSD, sd2i = Data\$NegativeUnrelatedSD, ni= Data\$`Number PP`, ri = Data\$Correlationwithin)

##transform variances to SEs
for (i in 1:nrow(Neutral)){
Neutral\$vi[i] <- sqrt(Neutral\$vi[i])
}

for (i in 1:nrow(Negative)){
Negative\$vi[i] <- sqrt(Negative\$vi[i])
}

##transform SEs to SDs
for (i in 1:nrow(Neutral)){
Neutral\$vi[i] <- Neutral\$vi[i] * sqrt(Data\$`Number PP`[i])
}

for (i in 1:nrow(Negative)){
Negative\$vi[i] <- Negative\$vi[i] * sqrt(Data\$`Number PP`[i])
}

##Calculate standardized emotion differences
NeutNeg <- escalc(measure = "SMCC", m1i = Neutral\$yi, m2i = Negative\$yi,
sd1i = Neutral\$vi, sd2i = Negative\$vi, ni= Data\$`Number PP`, ri = Data\$Correlationbetweenemotion)

Would this work like this? Or is there an easier way to calculate my effect size measure of interest?

Your help would be highly appreciated in this matter.
Thanks in advance, and kind regards,
Sera Wiechert

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