[viraptor]

Can you normalise data like that based on a confidence interval? Just rescaling the graph to unify them seems wrong, (it would answer something like "what do we think the distribution would look like if we distrusted the low end?") but maybe there's a better way?

[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)

[codesushi42]

A confidence interval is not what you want since this isn't a normal distribution of values.

Instead you'd want to use a CDF that bins that values.