You should do the convergence study on the measure that you are analysing.
If you are analysing strain, perform it on strain.
Mises on mises, max principal stress on ... you get the point. No idea why you would do it on the ratio of min/max principal, but if that is your application ...
Unaveraged should be always the case.
On integration points preferably (although if your mesh is converged most of the time the extrapolations to the points are 'good enough', esp. for linear calcs)