[R-meta] d_z and d_av effect sizes in metafor

[Zhouhan Jin]

Thank you, Wolfgang, for the clarification! Is it possible to share the formula for bias correction for SMCRP and how it is different from the correction factor used in SMCC or SMD? Any references for the difference in correction factors are highly appreciated?

Best wishes,

Zhouhan Jin
On Apr 7, 2025 at 07:18 -0400, Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl>, wrote:
Dear Zhouhan,

If r=0.5 *and* sd_pre = sd_post, *then* the SMCC and SMCR are identical:

n <- 30
r <- 0.5 # r set to 0.5 for demonstration
mean_pre <- 0
mean_post <- 0.5
sd_pre <- 0.75
sd_post <- 0.75

escalc(measure = "SMCC", m1i = mean_post, m2i = mean_pre,
sd1i = sd_post, sd2i = sd_pre, ri = r, ni = n)

escalc(measure = "SMCR", m1i = mean_post, m2i = mean_pre,
sd1i = sd_post, sd2i = sd_pre, ri = r, ni = n)

However, r=0.5 is not sufficient for this equivalence to hold.

Even then, SMCRP will be slightly different, since it uses a different bias-adjustment factor:

escalc(measure = "SMCRP", m1i = mean_post, m2i = mean_pre,
sd1i = sd_post, sd2i = sd_pre, ri = r, ni = n)

We can switch off the bias correction and then get equivalence for this measure as well:

escalc(measure = "SMCC", m1i = mean_post, m2i = mean_pre,
sd1i = sd_post, sd2i = sd_pre, ri = r, ni = n, correct=FALSE)

escalc(measure = "SMCR", m1i = mean_post, m2i = mean_pre,
sd1i = sd_post, sd2i = sd_pre, ri = r, ni = n, correct=FALSE)

escalc(measure = "SMCRP", m1i = mean_post, m2i = mean_pre,
sd1i = sd_post, sd2i = sd_pre, ri = r, ni = n, correct=FALSE)

The sampling variance will still be different for SMCRP, since it uses more information compared to SMCR.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf
Of Zhouhan Jin via R-sig-meta-analysis
Sent: Saturday, April 5, 2025 21:18
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-
project.org>
Cc: Zhouhan Jin <zjin65 using uwo.ca>
Subject: [R-meta] d_z and d_av effect sizes in metafor

Hello Wolfgang and Rmeta Community,

I always assumed that under pre-post correlation = 0.5, metafor::escal()'s
measure = "SMCC" and "SMCRP" referred to in the article below as "d_z" and
"d_av" respectively, are equivalent. But that doesn't seem to be the case (see R
code below).

Questions: 1- Can they be equivalent under any condition?
2- If yes, will their sampling variances then also be equal?
3- If no, are there any other two SMC variants that will be
equivalent in both effect size and sampling variances under r=0.5?

ARTICLE:
https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2013.0086
3/full

# R code:
library(metafor)
n <- 30
r <- 0.5 # r set to 0.5 for demonstration
mean_pre <- 0
mean_post <- 0.5
sd_pre <- 1
sd_post <- .5

esc_dz <- escalc(measure = "SMCC", m1i = mean_post, m2i = mean_pre,
sd1i = sd_post, sd2i = sd_pre, ri = r, ni = n)

esc_dav <- escalc(measure = "SMCRP", m1i = mean_post, m2i = mean_pre,
sd1i = sd_post, sd2i = sd_pre, ri = r, ni = n)

Best wishes,

Zhouhan Jin

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