[R-meta] I2 in fixed-effect or equal-effects meta-analysis

[Yefeng Yang]

Oops. Somehow, the incomplete email was sent out. I am so sorry for this.

The reproducible example:
library(metafor)
dat <- dat.bangertdrowns2004
# fixed-effect
res <- rma(yi, vi, data=dat, method="EE"), with the (partial) output:
Equal-Effects Model (k = 48)

I^2 (total heterogeneity / total variability):   56.12%
H^2 (total variability / sampling variability):  2.28

# random-effects
res2 <- rma(yi, vi, data=dat), with the (partial) output:
Random-Effects Model (k = 48; tau^2 estimator: REML)

tau^2 (estimated amount of total heterogeneity): 0.0499 (SE = 0.0197)
tau (square root of estimated tau^2 value):      0.2235
I^2 (total heterogeneity / total variability):   58.37%
H^2 (total variability / sampling variability):  2.40


# fixed-effects
res3 <- rma(yi, vi, data=dat, method="FE"), with the (partial) output:
Fixed-Effects Model (k = 48)

I^2 (total heterogeneity / total variability):   56.12%
H^2 (total variability / sampling variability):  2.28


All the best,
Yefeng

Yefeng Yang PhD
University of New South Wales, Sydney, Australia

________________________________
From: Yefeng Yang
Sent: Thursday, May 22, 2025 13:57
To: r-sig-meta-analysis using r-project.org <r-sig-meta-analysis using r-project.org>
Subject: I2 in fixed-effect or equal-effects meta-analysis

Dear community,

Recently, I played with the fixed-effect or equal-effects meta-analysis implemented in `metafor` package and surprinsly found that the model output provides I^2 value. To me this is a bit confusing, because the fixed-effect or equal-effects meta-analysis assumes that there is no heterogeneity (no tau^2 and so no I2). All observed differences in effect sizes are assumed to be due to sampling variance of the effect size estimates. Although one can computationally get I2 value from  fixed-effect or equal-effects meta-analysis via 100% * (Q-(k-1))/Q, but what does I2 exactly mean here?

Interestingly, the I2 provided by equal-effects meta-analysis is exactly the same as random-effects meta-analysis. The so-called fixed-effects meta-analysis (the true effect sizes are fixed across k studies rather than randomly drawn from a population) also gives I2.

The reproducible example:
library(metafor)
dat <- dat.bangertdrowns2004
# fixed-effect
res <- rma(yi, vi, data=dat, method="EE"), with the output:
Equal-Effects Model (k = 48)

I^2 (total heterogeneity / total variability):   56.12%
H^2 (total variability / sampling variability):  2.28

# random-effects
res2 <- rma(yi, vi, data=dat)

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