Since there is a dependency in the data (the same individuals were examined twice, therefore pre and post test scores are most likely correlated), I would advise against combining the pre and post scores as if they were independent observations from separate people. I would treat these as separate variables and address the outlier issue in a different way.

Hello Jeongwoon,

Much of the decision about "best" approach will depend on the specific research question(s) you seek to address, as well as the nature of the data (and how the data were collected). As we don't yet know this information, I'm having to give a general observation, based on what your query does contain.

I would suggest you consider using pre scores as a covariate and compare post scores by intervention method. If model residuals are troublesome here, you can easily apply bootstrap error estimates which do not require presumptions about distribution shape. Tests of the covariate in the model address whether pre- and post-scores are linearly associated.

If this is way off base for your research aims, perhaps you could elaborate your query.

Good luck with your work.

Great work

Great concept.