As others have pointed out, it is a good idea to encode domain knowledge in your time series model through specification and priors. Prophet rarely beats a well specified GLM or SARIMA in real world applications, especially when uncertainty estimates are needed. Professionally, I have succesfully applied Gaussian Processes to many such cases.
A GP is an intuitive and expressive way to code time covariance in a model. A famous example is the relative birthdays model, discussed by Gelman et al in Bayesian Data Analysis and here [1].
The biggest mistake engineers make is determining sample sizes. It is not trivial to determine the sample size for a trial without prior knowledge of effect sizes. Instead of waiting for a fixed sample size, I would recommend using a sequential testing framework: set a stopping condition and perform a test for each new batch of sample units.
This is called optional stopping and it is not possible using a classic t-test, since Type I and II errors are only valid at a determined sample size. However, other tests make it possible: see safe anytime-valid statistics [1, 2] or, simply, bayesian testing [3, 4].
I had a similar experience. I took psylocibin a few times, but after the last one I started getting panic attacks and feeling derealization quite often. This led to negative recurring thoughts and I felt really bad for a while. Got better after a year of cognitive behavioral therapy and six months taking a light dosage of antidepressants. Routine exercises and zen meditation helped tremendously as well. Get help, it is possible. Your brain can heal itself with your help.
I have a similar setup with Emacs + Evil + Poly + Quarto Modes. Evil for vim keybindings, Poly to read cells as buffers and Quarto as a superior alternative to Jupytext [1].
Multilevel models relax the assumption of independent observations by specifying that the measures of repeated experimental units are dependent on each other. It's a way of telling your model that it has less information than it would have if all observations came from independent units. Therefore, standard errors of effects are usually larger. Otherwise, they are biased [1].
Since most researches are not aware of multilevel models, they design their experiments and aggregate their data to fit the independence assumption, which is rarely a good idea. Many are not even aware of modeling beyond hypothesis tests, and are unable or unwilling to adjust their analysis for confounding factors or non-sampling errors that arise due to experiment design flaws.
Also, p-values should be deprecated, since a) nil hypothesis are strawmen at best and false by definition at worst [2] and b) they incentivize researchers to not think hard about effect sizes and uncertainty in their problems.
A GP is an intuitive and expressive way to code time covariance in a model. A famous example is the relative birthdays model, discussed by Gelman et al in Bayesian Data Analysis and here [1].
[1] https://avehtari.github.io/casestudies/Birthdays/birthdays.h...