Absolutely – there’s more involved than just corporal punishment. But psychologists do have a great deal of experience in teasing out the impact of particular issues, even when multiple issues are in place. It’s factor analysis – it’s a form of statistical mathematics expressly designed for this purpose.
Private schools don’t seem to have the same problems the state schools experience, they hung on to some of the more formal teaching methods and traditions.
Private schools generally don’t have the problems to the same extent, for a variety of reasons – but they still have them. A 25% increase in serious behavioural issues may not be anywhere near as dramatic as a 200% increase, but it’s still something to be avoided.