Say I'm doing stats on the height of adults from various countries.
I assume the heights of adults from one country are normally distributed, and ignore sex differences (I also ignore the fact that neighbouring countries tend to have similar populations).
I have a bunch of data by country, but for some countries I have very few data points, which can lead to quite big errors on my estimate of standard distributions.
Is there a way I can use the data from countries for which I have a lot of data to get better estimates - say if I notice standard deviation in those countries is always between 7 and 8.5 cm, but my dataset for Nepal (for which I have 9 samples) has a standard deviation of 9.5 cm, I should probably correct that downwards. But how? Is there a formula for this?
When calculating the parameters for Nepal, shouldn't the data from the other countries allow me to have a "prior" distribution of expected means and deviations, which I would then update by taking the actual data from Nepal into account? How would I formalize this methodology?
(I got this while looking for a simple reduction of the problem that prompted previous question, which didn't get an answer yet - I'm still mostly looking for good methodologies for thinking about this kind of problem).