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Comment by dfxm12 | Hacker News Reader

The fact that most stats is taught by getting students to just memorize random ideas rather than building up a holistic and intuitive view really is a travesty.

We don't need first principals thinking for every thing. Granted, this comment is a bit vague, so I don't know how exactly you were taught or which type of class we're talking about, but generally, you can accept some axioms in applied mathematics classes. If we're talking the bare minimum classes like in the article (for apparently a business degree), this is likely a general applied prob/stat. Things tend to get more in depth with more advanced pure mathematics courses.

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There's a middle path between rote memorization of outcomes, and building everything up from first principles. And I'm guessing it's probably what the parent poster had in mind.

A great statistics textbook along these lines is Principles of Statistics by MG Bulmer. It's one of those Dover classic textbooks that you can get for cheap. This book assumes you already know basic calculus and combinatorics. It then goes through a series of practical problems, and shows how you can use calculus or combinatorics to solve them. And, along the way, an intuitive and holistic perspective on statistics begins to form.

The overall effect is great. It's a lot like a 3blue1brown video series, only from the 1960s, and with problem sets.

I get where you're coming from, and obviously there are practical limitations on how deep one can and should go in an introductory class. But my recollection of AP Statistics 15 years ago is that, because the exam and therefore curriculum was so focused on running various tests on a TI-84, I learned way more about using this one specific graphing calculator than about statistics. I got a high score on the exam, but I never felt like I understood any of it until I got to college and took a statistics course that actually used calculus to show what was going on.

We don't need first principals thinking every time, but having an understanding of why you can't just test 100 variations of your hypothesis and accept p=0.05 as "statistically significant" is important.

Additionally it's quite useful to have the background to understand the differences between Pearson correlation and Spearman rank, or why you might want to use Welch's t-test vs students, etc.

Not that you should know all of these things off the top of your head necessarily, but you should have the foundation to be able to quickly learn them, and you should know what assumptions the tests you're using actually make.

Intuition isn’t synonymous with working from first principles. You can have a very intuitive understanding of something you only understand at a higher level. Indeed, this is true for many applied mathematicians.

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