How do I obtain a pooled mean standard error?
Suppose we have each of K people (or groups) which we wish to pool each with variances, $V_text{k}$ and mean $m_text{k}$ based on a sample of size $n_text{k}$.
$$ Pooled Variance V = \frac{\sum_text{k}(n_text{k}-1)V_text{k}}{\sum_text{k}(n_text{k}-1)} $$
$$ Pooled Mean Standard Error = \sqrt{V / \sum_text{k} n_text{k}}