Circular data are a natural outcome in many biomedical studies, e.g. some measurements in ophthalmologic studies, degrees of rotation of hand or waist, etc. With reference to a real data set on astigmatism induced in two types of cataract surgeries we carry out some two-sample testing problems with the possibility of common or different concentration parameters in the circular set up. Detailed simulation study and the analysis of the data set, including redesigning the cataract surgery data, are carried out.