Output too similar from FE and REML model meta-analysis on metafor for R

Question

I'm trying to use the metafor package in R to run fixed and random effects model meta-analyses on data with a single continuous variable. I'm using restricted maximum likelihood estimation for the random effects model. The problem I'm having is that the output for the random effects model (specifically, the effect size, standard error, CIs, z, and Q) are 9 times out of 10 the exact same stats I get from running the fixed effects model.

I was expecting every stat other than the effect sizes to vary between models most of the time. Can you explain to me why this is not the case?

Thanks very much!

data(dat)
dat <- escalc(measure = "SMD", data = dat, 
           n1i = T2_N,
           n2i = T1_N,
           m1i = T2_Mean,
           m2i = T1_Mean,
           sd1i = T2_SD,
           sd2i = T1_SD)

dat_FE <- rma(data = dat, measure = "GEN", method = "FE", yi = yi, vi = vi)
dat_REML <- rma(data = dat, measure = "GEN", method = "REML", yi = yi, vi = vi)

Answer 1

If the estimate of $\tau^2$ is 0, then the results will be identical. And the Q-statistic is always computed under the null (i.e. under $\tau^2= 0$), so the value will always be the same.