# Meta analysis: is there such a thing as too little heterogeneity?

First time I've seen results like these and they make me feel uneasy. Is it even appropriate to do a meta-analysis here? Even my poor forest and funnel plots are messed up.

> results <- rma(yi, vi, data=meta)
> results

Random-Effects Model (k = 13; tau^2 estimator: REML)

tau^2 (estimated amount of total heterogeneity): 0 (SE = 0.0043)
tau (square root of estimated tau^2 value):      0
I^2 (total heterogeneity / total variability):   0.00%
H^2 (total variability / sampling variability):  1.00

Test for Heterogeneity:
Q(df = 12) = 7.0093, p-val = 0.8570

Model Results:

estimate      se     zval    pval   ci.lb   ci.ub
0.8101  0.0318  25.5163  <.0001  0.7479  0.8724  ***

---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> predict(results, digits=3, transf=transf.ztor)
pred ci.lb ci.ub cr.lb cr.ub
0.670 0.634 0.703 0.634 0.703
> confint(results)

estimate  ci.lb   ci.ub
tau^2    0.0000 0.0000  0.0123
tau      0.0000 0.0000  0.1107
I^2(%)   0.0000 0.0000 41.8957
H^2      1.0000 1.0000  1.7210


• Worth noting that the 95% ci for $I^2$ is only about half the width of the 100% ci from 0 to 100 so your estimate of $I^2$ is quite imprecise. – mdewey Aug 21 '18 at 12:47

Each study has a high standard error, translating to wide confidence intervals. This could be due to low sample size or high within-study variability. The results of your meta-analysis indicate no between-study heterogeneity, evidence by the estimate for $\tau^2 \approx 0$. This is sensible given that the within-study variability seems to mask (is much larger than) any apparent between-study variability.