stan VS tests-as-linear

Alternatives: stan and edward

remove.packages(c("StanHeaders", "rstan")) install.packages("rstan", repos = c("https://mc-stan.org/r-packages/", getOption("repos")))

My approach to problems like this is to write down the proposed model mathematically first, in extreme detail. I find hierarchical form to be the easiest way to break it down piece by piece. Once I have the maths then I turn it into a Stan model. Last step is to use the Stan output to answer the research questions.

Here is a good breakdown of recommendations from Andrew Gelman.

For instance my first choice in these cases is always a Bayesian inference tool like Stan. In my experience as someone who’s more of a programmer than mathematician/statistician, Bayesian tools like this make it much easier to not accidentally fool yourself with assumptions, and they can be pretty good at catching statistical mistakes.

I tend to be most impressed by tools and libraries. The stuff that has most impressed me in my time in ML is stuff like pytorch and Stan, tools that allow expression of a wide variety of statistical (and ML, DL models, if you believe there's a distinction) models and inference from those models. These are the things that have had the largest effect in my own work, not in the sense of just using these tools, but learning from their design and emulating what makes them successful.

oh its certainly used in practice. you should look into frameworks like Stan[1] and pyro[2]. i think bayesian models are seen as more explainable so they will be used in industries that value that sort of thing

[1] https://mc-stan.org/

I knew the linked-in-the-article https://lindeloev.github.io/tests-as-linear/ 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

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 t-tests 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/tests-as-linear/ ). 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 "t-test-vs-anova" because they're the same thing anyways.

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/tests-as-linear/#41_one_sample_t...

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/tests-as-linear/

Most parametric tests don’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 isn’t normal, as cool as they are. (Also a pedantic nitpick: Mann-Whitney and Co. test difference in average ranks, not difference in means. So they are not really a nonparametric equivalent to T tests).

I think this is what you are looking for: https://lindeloev.github.io/tests-as-linear/