[le0n]

A confidence interval won't adjust the points (point estimates) but will give those points with a lower sample size wide confidence intervals (often covering zero).

Using an (empirical) Bayesian multilevel model can both attach uncertainty intervals to the point estimates and appropriately "shrink" the estimates towards zero at the low-sample-size end.

The latter is more directly interpretable, at the cost of slightly more complex modelling (/assumptions).

[viraptor]

Thanks! I think the shrinking you mention is what I was trying to say :)

Looking for explanation of multilevel model, I found http://mc-stan.org/documentation/case-studies/radon.html which seems to do exactly that in "Partial pooling model". (see graph)