# Overall confidence interval from multiple samples

#### coloradikal

##### New Member
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!

#### hlsmith

##### 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?

#### hlsmith

##### 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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#### katxt

##### 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.

#### hlsmith

##### 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.

#### coloradikal

##### New Member
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.