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Python port of "Common statistical tests are linear models" by Jonas Kristoffer LindelÃ¸v. (by minireference)

testsaslinear discussion
testsaslinear reviews and mentions

The Truth About Linear Regression
1) All common statistical tests are linear models: https://lindeloev.github.io/testsaslinear/
 Common statistical tests are linear models (or: how to teach stats)

Everything Is a Linear Model
I knew the linkedinthearticle https://lindeloev.github.io/testsaslinear/ which is also great. A bit meta on the widespread use of linear models: "Transcending General Linear Reality" by Andrew Abbott, DOI:10.2307/202114

Bayesians Moving from Defense to Offense
Maybe you would find it useful to read a textbook on bayesian stats for inspiration. I can recommend Richard McElreath's "Statistical Rethinking" which makes it very clear how inflexible it is to just know recipes like ttests or anovas.
The canonical approach is to build a generative model with a parameter (or multiple for ~anova) that codes for the difference between groups and do inference on that parameter of interest. Most of the recipes taught in statistics classes can be modelled as a regression of some kind (this counts for frequentist stats too, see https://lindeloev.github.io/testsaslinear/ ). Some advocate to do that inference with bayes factors. Others, like discussed elsewhere in this thread, advocate combining the resulting posterior with a cost/value function, but either way the lesson is that there is less focus on "ttestvsanova" because they're the same thing anyways.
 How to cheat stats: common statistical tests are linear models

Introduction to Modern Statistics
I understand where you're coming from, and I like the idea for a certain kind of people: those who are very good at handling abstractions. Software engineers do have this skill, but the majority of statistics users do not. Trying to explain the similarities between these linear methods and how all is one [1] to a social scientist who doesn't like numbers nor formulas to begin with would only lead to more confusion.
But if you ever do a randomized test with a suitable linear model to estimate the efficacy of these two methods, do let us know, that would be 10/10 :)
[1]: https://lindeloev.github.io/testsaslinear/#41_one_sample_t...
 [Statistics and Probability] Common statistical tests are linear models (or: how to teach stats)

[Q] Critique of a flowchart I made?
My main critique is that these classical tests are often better explained and introduced in the concept of a regression framework. The fact that you even need a flowchart demonstrates how confusing and unintuitive the classical approach to teaching statistics is. If you learn regression, everything else becomes a special case of this much more expressive way of thinking about how to measure variation. This point is made convincingly in this post: https://lindeloev.github.io/testsaslinear/

[Q] Two questions concerning the relationship between nonparametric tools and normal distribution
Most parametric tests donâ€™t assume normality. If you feel that assuming normality is not viable, you are free to choose any other distribution. This may not be immediately obvious, since most intro courses teach inference as a bunch of disjointed formulas, but it will make more sense once one learns about generalized linear models framework and realizes that common statistical tests are all linear models. There is no need to jump straight for nonparametric tests just because something isnâ€™t normal, as cool as they are. (Also a pedantic nitpick: MannWhitney and Co. test difference in average ranks, not difference in means. So they are not really a nonparametric equivalent to T tests).

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Stats
The primary programming language of testsaslinear is JavaScript.