I don't think your claim is possible to prove statistically - what does "pure reason" mean? And of course it's *pure reason + empirical observatoons," since even if they're not running experiments they still see natural phenomena.
Pure reason is conjecture with little empirical input (and big intuitive or memey input) and little verification of output, i.e. a large deviation from empiricism.
> There is no scientific proof that the scientific method is valid.
The scientific method is provably effective in a lawful world. That the scientific method isn't provably effective is because the world is not provably lawful ... it's logically possible for the "laws" of physics--which are simply regularities that we have discovered--to suddenly change, oscillate, be random, etc. But as long as they don't the scientific method works ... and we can't do better. (Not in this world, anyway ... in some other world there might be oracles (aka gods or bibles) that always have the right answer and we could simply query them. Of course, such oracles are also not provably correct.)
The attitude of "we can't do better" is precisely the kind of attitude that would have hampered the creation of various sciences and their methods in the first place, and the production of scientific thought is often not as pure or logically consistent as all the methodological purists or Popperians seem to believe it is. Feyerabend, Quine, Von Foerster, Dataon and Gallison and several others have made this pretty clear and make the argument pretty forcefully in my opinion.
All sciences carry an ontology and value system along with them. Religion is also a rich and highly effective epistemic structure when your underlying ontological assumptions, values, and goals differ from those established and implicit in the scientific (predominantly utilitarian) Western enlightenment value system. Science is not able to found itself on some irrefutable bedrock "truth" correspondence any more than religion is. There is no basis by which we can actually solidify empiricism as somehow more privileged and more capital T true if we admit the possibility of human error.
This lie is so tiresome.
It's notable that science has a history of effectively producing confirmable fact whereas religion produces only falsehoods.
There is a sense in which all of my observations hence will be "theory laden". When I seek "proof" i'm likely to do so within the constraints of fabulashinaism.
Science proceeds in the same way. Only crises, which are unpredictable and may have much more than simple "new data collected" behind them actually drive theory change. Beyond the theoretical assumptions, many of which are not proven but are constraining hypotheses, there are the social value assumptions I mentioned as well. As someone else said in the thread, science cannot prove science. You can be of the opinion that it's been more effective than alternatives, and I would agree, but there is no way to prove this because it is ultimately a question of theoretical assumptions and of values.