We are sampling the rates of $n$ elevators rising up floors in order to see which elevators are the fastest, and which are the slowest. Say we have $k$ time samples from each elevator, $S_1, S_2, ... , S_n$, where $S_j$ is a data set of samples for the $j$th elevator $$ S_j = (x_1,x_2,...,x_k) $$
Now we know how to test say if $\mu_1 < \mu_2$ using a t-test, however we are not sure how to come up with the most likely ordering of means given the data. From there can we calculate our confidence in the estimate?
Any help would be appreciated