Appreciating R: The Ease of Testing Linear Model Assumptions (opens in new tab)

R (and its predecessor S) is so great, thank you for writing and sharing this!

In a way, R is very similar to APL and J in that many operations automatically scale from scalars to vectors, and you can therefore conveniently express applications of operations to many elements at once. In fact, even its assignment operator is chosen to syntactically resemble that of APL:

https://blog.revolutionanalytics.com/2008/12/use-equals-or-a...

Regarding the quote:

"All statistical models and tests have underlying mathematical assumptions on the types of conditions upon we can generate reliable results (Hoekstra et al., 2012)."

Indeed! There is hence also a very close connection between statistics and logic.

Have I gone overboard in remembering that Gauss-Markov is overrated? It's nice that some assumptions guarantee BLUE, but then there is real world data and modelling. Understand where your data come from, what distributions they have, what the relationship is with your dependent variable. Testing for these assumptions might be helpful as a teaching tool, but please get to the level to be able to demonstrate that your model can fail a few of these (like heteroskedacity) and still work (or recognize you need more than a linear model).

It's not surprising that R has good tools for statistical assumptions checking. It has everything with an API perfectly suited for stats professionals. In the Python world scipy and statsmodels implement most of the important tests, but probably not as many as the ones available in R.

One recent project that I looks very promising in the Python world is called Tea: a high-level language for expressing statistical analysis questions. Basically the user describes the characteristics of the data they have, their assumptions, and their hypothesis, and then the tea runtime checks all the assumptions and figures out which test can be applied to test the hypothesis. You still have to know some stats jargon, but the user-interface between human and machine is revolutionary! Here is a bunch of links I collected about tea: https://www.one-tab.com/page/aUF1eWnDT8CIyrwScWD2uA