Having taught in both the state sector and the private – I can tell you that, for me, the single largest reason why state schools get poorer results is that the independent sector is considerably less tolerant of failure.
Having been educated in both systems, I think this is much more down to the high quality of teaching & other resources in the private sector. A class of 15 is a very different beast from a class of 30. The private sector probably demands higher standards and sets higher expectations but it also has a far greater chance of achieving them. Failure is relative.
Just shouting at people as a motivational tactic is antediluvian.