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It's funny because statisticians are among the loudest critics of how easily statistics can be abused. I encourage you not to be turned away from a whole field because one bad representative. Professors are humans too and say a lot of dumb things. Very few are their field incarnate.

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STATISTICIANS actually do fine, generally. The problem is that no statisticians were involved in the analysis and write-up of almost all research that isn't statistics papers.

The statistics just don't mean what most scientists think/write they mean. They're using em wrong. As the OP explains some manners of, in fairly technical language.

Statisticians are doing fine indeed. The problem lies entirely in the ( non) design of experiments ( DoE) of the “scientists”. The sorry state of affairs of graduates from universities in properly designing experiments in which proper randomization, focus on sources of variability, between groups and within groups is not understood nor accounted for in the design is the true source of the problem. Scientists should always consult a statistician when undertaking an experiment. At least if they would like to make/draw sensible conclusions.

Yes, I was just saying along with OP that a statistician would be most critical of the professor's reasoning. It's like a tyrant saying you should take a class in morals when you raise an objection to their atrocities.

What do Bayesians say these days btw?

I still find Bayes to be more grounded and less “pie in the sky” than frequentists.

It all depends on your priors what they say. :)

But seriously, you can have the most pathological prior distribution, so you can then stick with it forever. (Let's say your prior predestines you to always find that whatever the new piece of data you get is so unlikely that it's more likely that it's an error/conspiracy than a real piece of data that you have to do belief update on.)

So, instead of coming up with a significance level, you have to estimate the chance of observing a null result, which determines how much new data moves your posterior distribution. The "advantage" of the Bayesian approach is that - in theory - you can incorporate every tiny little bit of data into your model (distribution). The disadvantage is, that it's very susceptible to various biases (through a biased prior).

Bayesian statistics are mathematically perfect, as long as your priors are true. Unfortunately, they are not.

I think it’s the opposite. Your confidence intervals are only true if your distribution is true. But how can it be that perfect? At least Bayesians adjust their knowledge like scientists.

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