Once the author started taking pills independently of their stress level, the variance of differences diminished a lot. I'd wager this supports the mean reversion hypothesis.
Also, while I agree with their general conclusion that theanine probably doesn't reduce stress, I'd give assign more probability to the hypothesis that theanine does work, but in other design settings. For example: drinking tea instead of taking pills, or measuring stress levels after a day instead of an hour, or evaluating the difference across time instead of in time chunks.
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.
Thank you, I'm aware of this. But I don't understand how your link answers my previous message. I was asking for example of how to fit it using only aggregated statistics (focus on "aggregated"). I'm afraid the MCMC or other Bayesian sampling algorithms are not the right examples.
For anyone interested in anytime-valid testing, I wrote a Python library [1] implementing multinomial and time inhomogeneous Bernoulli / Poisson process tests based in [2].
