I have two samples with a mean and SE for each. I want to combine them, so how do I calculate a combined standard error when combining two samples means? I can only find information about combining means and SD's at the moment.
Solved – Combining samples based off mean and standard error
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Best Answer
If your first population has mean $\mu_1$ and variance $\sigma_1^2,$ then the sample mean ${\bar{x}_1}$ of your data has variance ${\sigma_1^2 \over n_1},$ where $n_1$ is the sample size. Similarly for your second sample the variance of the sample mean ${\bar{x}_2}$ is ${\sigma_2^2 \over n_2}.$
The variance of the combined sample mean ${\frac{1}{2}}\left(\bar{x}_1+\bar{x}_2\right)$ is then ${\frac{1}{4}}\left({\sigma_1^2 \over n_1}+{\sigma_2^2 \over n_2}\right).$
So its standard deviation is ${\frac{1}{2}}\sqrt{{\sigma_1^2 \over n_1}+{\sigma_2^2 \over n_2}}$
The standard error, which is an estimate of this standard deviation, is given by ${\frac{1}{2}}\sqrt{{s_1^2 \over n_1}+{s_2^2 \over n_2}},$ where $s_1$ and $s_2$ are the sample standard deviations.
Note that this is for a simple average of the two sample means, not a weighted version.