The burden of proof is generally on the person standing up and making a claim, no matter how obvious the claim is or which side they're trying to prove.
But even when two people make opposite claims and there's no good consensus either way, trying to assign burden of proof by what seems obvious or reasonable isn't a solution. That just takes you back to two people disagreeing about what is obvious or reasonable, it's just going in circles.
Something you can do instead is put burden of proof on the person deviating from the null hypothesis, because everyone can agree on that. Crucially, the null hypothesis does *not* mean the obvious thing, or the expected thing.
In the case of whether breathing is fundamental and healthy, the null hypothesis is that breathing does absolutely nothing. And of course it's not very hard to reject that one, the null hypothesis is clearly wrong here. If it really is obvious, then you shouldn't have a hard time rejecting it and all is right in the world.
But trying to make a claim that's not so easy to prove, and at the same time trying to escape the burden of proof because it 'seems obvious or at least reasonable' harms your ability to notice when you're wrong. It's dangerous and it's bad epistemology.
Correct me if I'm wrong but you can state the null hypothesis arbitrarily: "Breathing does nothing" / "Not breathing does nothing." "Aerobic exercise does not increase the probability of developing metastatic cancer" / "A sedentary lifestyle does not increase the probability of developing metastatic cancer." So, in fact your null hypothesis already has a bias of what you consider the baseline, i.e. yes-cancer or no-cancer. So in essence, you are trying to scientize for the sake of argumentation.
>"Breathing does nothing" / "Not breathing does nothing."
Right, but that's because those two are actually the same! The null hypothesis in this case does not directly say whether breathing is good or bad, instead it's a statement about the correlation of breathing to anything at all.
If the null hypothesis is true, then breathing or not breathing doesn't have any effect. So the null hypothesis is not pro-breathing or anti-breathing, the null hypothesis is that it just doesn't matter either way and doesn't correlate with anything (like the person staying alive)
>"Aerobic exercise does not increase the probability of developing metastatic cancer" / "A sedentary lifestyle does not increase the probability of developing metastatic cancer."
With both of those, you can also reformulate them to be a statement about correlation. "What is the correlation between the amount of aerobic exercise that you do and the rate of development of metastatic cancer?"
So the null hypothesis doesn't depend on whether you think exercise is good or bad. That's the subtlety. It just says that everything is neutral and nothing has any effect until proven otherwise.
That doesn't mean the null hypothesis is always what makes sense, or that it's what you should believe in. Obviously breathing keeps you alive, and exercise has a lot of benefits. It's just a way to keep people from disagreeing about what's obvious and who should prove what. The null hypothesis is really dumb, and it only says that anyone who claims they found a real effect, either good or bad, should prove it.
If one person is saying red wine causes cancer, and the other person is saying red wine prevents cancer, then they're both rejecting the null hypothesis, which is that you can't claim red wine correlate with anything until proven otherwise.
And I promise this isn't just for the sake of the argument. There's a real difference between the mindset of trying to claim "X is good" or "X causes cancer" because it seems so obvious that someone else should just prove the opposite instead, and the much more boring idea that if something is actually kind of obvious, then you should be able to measure whether it does anything AT ALL in either direction (good or bad), and force the person actually making the claim to reject the null hypothesis.
As I understand it, correlation is not sufficient to prove causation. "Null hypothesis" is one statistical tool, an abstraction over our understanding of the real world.
Consider the case where all of those infected with disease D die, while 99% of those infected with D and treated with T survive. Further consider that T is widely administered. Clearly, the correlation between being infected and dying is very low although with a deeper understanding we know that D in fact causes death.
>As I understand it, correlation is not sufficient to prove causation. "Null hypothesis" is one statistical tool, an abstraction over our understanding of the real world.
Absolutely. The only reason we use it is because most of the other alternatives turned out to be not that great in practice, but it has plenty of limitations to keep in mind (like correlation != causation, but also the common p-hacking that happens, etc etc).
>Clearly, the correlation between being infected and dying is very low although with a deeper understanding we know that D in fact causes death.
That's true, although working back from just the people who die and focusing on those, the method is eventually able to unearth the correlation too. With the people who die, we would naturally start to ask why them? Did they do anything differently than the rest of the population? We'd see pretty quickly that there was one huge factor in common, which is that none of them were using T.
I'll admit that's not enough to say just looking at correlations and trying to disprove nulls is going to be enough in every case. I would just say it's a pretty good starting point when people disagree on a fundamental level about what should be obvious, or who should be proving what. It's really kind of dumb, but in practice in the case of people missing something (most deficiencies, like not having enough vitamin B12, or not having enough thyroid hormone) stats do a pretty good job of noticing that all the people dying mysteriously happen to be missing the same thing. (But of course it misses plenty of things too. And where it gets a lot harder is understanding why any of this happens)
But even when two people make opposite claims and there's no good consensus either way, trying to assign burden of proof by what seems obvious or reasonable isn't a solution. That just takes you back to two people disagreeing about what is obvious or reasonable, it's just going in circles.
Something you can do instead is put burden of proof on the person deviating from the null hypothesis, because everyone can agree on that. Crucially, the null hypothesis does *not* mean the obvious thing, or the expected thing.
In the case of whether breathing is fundamental and healthy, the null hypothesis is that breathing does absolutely nothing. And of course it's not very hard to reject that one, the null hypothesis is clearly wrong here. If it really is obvious, then you shouldn't have a hard time rejecting it and all is right in the world.
But trying to make a claim that's not so easy to prove, and at the same time trying to escape the burden of proof because it 'seems obvious or at least reasonable' harms your ability to notice when you're wrong. It's dangerous and it's bad epistemology.