I am currently simulating a molecule and need to calculate the global mean value and more specifically the error of the global mean of a parameter $r$ denoting its size. To do that I have a multiple of $N=10$ runs, each having $n=10.000$ data points $r_i^j$ - where an upper index denotes the run and a lower the data point inside run $j$. Due to the "high" sampling frequency I can assure that there is correlation between the data points $r_i$ in a given run. That is why i think I cannot use the answer given in a similar question (Calculating statistic for multiple runs). So my questions are:
1.) Does the correlation really make a difference in calculating the error of the global mean value?
2.) If so what is the correct way to compute the global mean?
By discussion with colleagues I think the appropriate way would be to calculate the $\bar{r}^j$ and $\sigma^j$ for each run and then look at the distribution of $\bar{r}^j$ to calculate its standard deviation and standard error.