It's problematic to say that scientists have 'proved' anything. Scientist's conclusions are always based on the available data, and at any point new data may come along that disproves their conclusion. Scientists know this of course, which is why reputable ones are never going to step forward and announce "I have proved..."
https://en.wikipedia.org/wiki/Scientific_evidence
> evidence cannot prove a theory correct because other evidence, yet to be discovered, may exist that is inconsistent with the theory
When I use the word "prove" i don't mean like proving things in math. Nobody means this, it's obvious to everyone what they mean. Prove in this context means well established. For example if I say scientists have proved the theory of gravity.
What's going on here is extreme pedantry. Prove has meaning in different contexts, you have chosen the most technical pedantic context to suit some misguided purpose rather than the most obvious context. There's no point in taking this further.
However you are referring to a social science when you talk about differences between kids of different generations. I think using 'proved' in that context puts you on pretty shakey ground.
What this means is that whenever you use the word "prove" with "science" it is colloquial. It is always colloquial.
The statistical methods used in social sciences are no different than the statistical methods used to "prove" things in physics.
This is science and its about research that the scientist did to prove something.