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> He told me experiments continued until they observed a statistically significant difference between the two conditions.

Apparently, if you do the observing the right way, that is a sound way to do that. https://en.wikipedia.org/wiki/E-values:

“We say that testing based on e-values remains safe (Type-I valid) under optional continuation.”

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This is correct. There's been a lot of interest in e-values and non-parametric confidence sequences in recent literature. It's usually refered to as anytime-valid inference [1]. Evan Miller explored a similar idea in [2]. For some practical examples, see my Python library [3] implementing multinomial and time inhomogeneous Bernoulli / Poisson process tests based in [4]. See [5] for linear models / t-tests.

[1] https://arxiv.org/abs/2210.0194

[2] https://www.evanmiller.org/sequential-ab-testing.html

[3] https://github.com/assuncaolfi/savvi/

[4] https://openreview.net/forum?id=a4zg0jiuVi

[5] https://arxiv.org/abs/2210.08589

Did you link the thing that you intended to for [1]? I can't find anything about "anytime-valid inference" there.

Thanks for noting! This is the right link for [1]: https://arxiv.org/abs/2210.01948

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