How can saying false things make your science "about the the real world"? The only thing I can think of is that by "real world" you are referring to using the publication of massive amounts of incorrect/questionable information as a metric for success. Yes, that is indeed the sham going on.
>"There is a reason humans naturally and instinctively do it when they talk about experiments. This is how you describe things in real world human language."
I have no problem talking about data without transposing the conditional, if you do that is some issue with your training.
>"Sure there are debates about priors."
The error you advocate (of transposing the conditional) has nothing to do with priors.
Also P(A|B) = P(B|A) if the prior probabilities are equal, often a reasonable prior.
Ok, but I fail to see the relevance of this to anything.
>"Also P(A|B) = P(B|A) if the prior probabilities are equal, often a reasonable prior."
Here, A = Hypothesis and B = data (or vice versa). You are claiming that the "probability of seeing your data whether or not the hypothesis is correct", is often near the "probability the hypothesis is correct independent of your data"?
Based on what? What principle leads you to think these two probabilities should be near each other? BTW, if you actually have one this is like the holy grail of statistics.
Shouldn't that be "the probability of seeing the data, _given_ that the hypothesis is correct" and "the probability of the hypothesis being correct, _given_ that the data has been observed"?
The claim is that it is reasonable to assume P(A) ~ P(B), so that P(A|B) ~ P(B|A). I am referring to P(A) and P(B) in the equation.
I agree there are debates surrounding priors, especially when you get into higher order, meta or purely hypothetical territory (there is no actual noise generator here) like this, but I think these are unavoidable.
For this to be true, P(observations) ~ P(pure noise generator) as you said earlier. Anyway, you can look at it from either perspective, doesn't really matter.
On what basis do you claim this is reasonable to expect? I suspect you have none whatsoever... in fact simple thought experiments will lead us to the opposite conclusion, and there is plenty of data telling us the same.
Sure there are debates about priors. These are unavoidable. The hidden assumption in my example is a 50/50 prior on too noisy, not too noisy hypotheses. IMO a reasonable uniform (maximum entropy) prior to start a discussion from. Of course, one should be more precise when doing this type of analysis in a paper. The reason a good prior is hard to define here is not because you shouldn't do the flip, it is because the question that the t-test is trying to answer doesn't make much sense.