Overall confidence interval from multiple samples

Hello! This is my first post on this forum. I've searched previous posts but can't find an answer to my question.

I have 12 stratified samples covering different areas of a population. I know how to calculate the point estimate (PE) and confidence interval (CI) for each sample. I also know how to calculate the overall PE. However, I need to also calculate an overall confidence interval.

How do I calculate an overall CI that represents multiple samples? Do I simply calculate the CI for each separate sample and then sum them all to derive the overall lower and upper boundary?

Thank you!


Less is more. Stay pure. Stay poor.
Good question. I am imagining the different areas have difference subsample sizes, requiring a weighting? Does this sound like what you are interested in and how you got your mean of means calculation?


Less is more. Stay pure. Stay poor.
Given you aren't assuming equal stds between sub-samples, the standard error is something like the following:

Sqrt [(Std_1^2 / n_1) +...+(Std_12^2 / n_12)]

then take your PE +/- SE(alpha value [e.g., 1.96)]

Look to the meta-analysis field for instructions.
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Active Member
Perhaps some squares in there? or else it is dimensionally inconsistent. Here is a formula from Wikipedia. Square root and make your CI.


Less is more. Stay pure. Stay poor.
Good eye @katxt - Above I had std not variances in the formula. I have now corrected this. This is the formula typically used in meta-analyses.
Most excellent -- thank you both for the input! I was heading in the general direction but these details are very helpful. I'll post more in a few days if I hit another roadblock.