# [R-meta] Further question on data extraction

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Mon Aug 24 15:08:31 CEST 2020

```Hi Tobias,

You could just do:

escalc(measure="SMD", m1i=48+29.7, m2i=47.3+26.7, sd1i=15, sd2i=19.4, n1i=43, n2i=41)

So that would be d = (mean1_post - mean2_post) / SD_pooled_pre.

Alternatively, one could compute the difference between the standardized mean changes (using raw score standardization). And since you know the baseline SD and the change score SD, you can back-calculate the correlation (under the sd1i = sd2i assumption).

SDchange1 <- (sqrt(43)*(34.7-24.7))/(2*qt(.975, df=43-1))
SDchange2 <- (sqrt(41)*(31.8-21.6))/(2*qt(.975, df=41-1)) # check the n for group 2

So (again using simple algebra):

r1 <- 1 - SDchange1^2 / (2*15^2)
r2 <- 1 - SDchange2^2 / (2*19.4^2)

And then:

dat1 <- escalc(measure="SMCR", m1i=29.7, m2i=0, sd1i=15,   ni=43, ri=r1)
dat2 <- escalc(measure="SMCR", m1i=26.7, m2i=0, sd1i=19.4, ni=41, ri=r2)

dat <- data.frame(yi = dat1\$yi - dat2\$yi, vi = dat1\$vi + dat2\$vi)
dat

So that would be d = (mean1_post - mean1_pre) / SD1_pre - (mean2_post - mean2_pre) / SD2_pre.

The values are actually quite different here (d = .21 vs d = .59), but they are both 'acceptable' SMD values. I cannot tell you which one to use, but see Morris and DeShon (2002) for a discussion of the difference. I would also consider what the majority of studies report/provide. If they are more along the lines of the first d-type, then I would go with that.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org]
>On Behalf Of Tobias Saueressig
>Sent: Monday, 24 August, 2020 13:57
>To: r-sig-meta-analysisr-project.org
>Subject: [R-meta] Further question on data extraction
>
>Hello,
>
>I have one more question on data extraction:
>
>I have two groups n1 = 43 and n2 = 41
>
>Baseline values (mean, SD): 48 (15) and 47.3 (19.4)
>Change within-group (mean, 95%CI): 29.7 (24.7 to 34.7) and 26.7 (21.6 to
>31.8)
>Difference between group changes (meandiff, 95%CI, pvalue): −3.0 (−10.1 to
>4.1) 0.4087
>
>I would do the following:
>
>SDchange1 <- (sqrt(43)*(34.7-24.7))/(2*qt(.975, df=43-1))
>SDchange2 <- (sqrt(44)*(31.8-21.6))/(2*qt(.975, df=43-1))
>
>Assume: SD of change scores = SD * sqrt(2*(1-r)) with r =0.9
>
>SD1prepost <- ((sqrt(43)*(34.7-24.7))/(2*qt(.975, df=43-1)))/sqrt(0.2)
>SD1prepost
>SD2prepost <- (sqrt(44)*(31.8-21.6))/(2*qt(.975, df=41-1))/sqrt(0.2)
>SD2prepost
>
>require(metafor)
>
>postmean1= 77.7 and postmean2 = 74
>
>summary(escalc(measure="SMD", m1i=77.7, sd1i=SD1prepost, m2i=74,
>sd2i=SD2prepost, n1i=43, n2i=41))
>