Let's say that we are measuring the tracking position error of two controllers and we want to know if both controllers are similar (we already perform a "differences" test but we are requested to perform an equivalence test).
For example, if the mean $\mu$ (in meters) of one controller (12 samples) is 0.00344 (standard deviation $\sigma=0.0006481424$), the other (12 samples) is 0.00331 ($\sigma=0.000498$).
If $\varepsilon$ is the magnitude of region similarity. How do we define this $\varepsilon$?
I could consider $\varepsilon$ as $N \cdot \sigma$ as the region of similarity so, for example if $N=3$ then $\varepsilon=3\cdot(0.00064)=0.0019$ (using the data of the first controller).
Or, I could use something like $\varepsilon=\mu \cdot 0.05$, this takes 5% of the mean (of the first controller) which gives $\varepsilon = 0.0172$.
The question is, should we use the data for controller 1 or 2---as in the previous options---to define this parameter; or should do we consider other kind of difference measure between them in order to determine the epsilon parameter?.
Finally, why not use the epsilon as a 0.9 which may indicate that the 90% of the 'data (or the area of the distribution)' should be similiar?
I appreciate any advice in order to determine the epsilon.
Please see e.g. the function here: