Statistical tests with data (n, mean and std values)

[deleted_user]

If I have a data describing different trials and for each trial I have: mean, std and number of considered events; how can calculate total mean, total std and further statistics tests (e.g. in a crossover design, ANOVA, ...).

Example

id mode sequence time reaction_mean reaction_std reaction_n
111 TOT A 1 1.34 .03 5
222 AXO B 2 0.3 1.5 2
333 TOT A 1 5.3 0 1
....

And now I want to make the statistics of each mode: TOT, AXO, ...