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

[Yefeng Yang]

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)

	[[alternative HTML version deleted]]