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I've had similar thoughts, but I think its more to do with what is in your head at the time you hear about it. I found permutation tests satisfying to learn abo

I've had similar thoughts, but I think its more to do with what is in your head at the time you hear about it. I found permutation tests satisfying to learn about because they somehow helped consolidate what I knew from distribution theory. If I didn't know any distribution theory prior, I'm not sure they could have that effect. If you study mathematical statistics, it is not taught as a cookbook. At the elementary level you learn probability theory and distribution theory, all the different distributions, hypothesis tests, regression, ANOVA and so on proceed from there. Meanwhile, I think research scientists are often taught statistics as a set of recipes because its usually a short course for a specific discipline. E.g. Statistics for biologists.

ImaCake 3y ago
I think those short courses would be more effective if they didn't bother with ANOVA and instead taught intro probability and distributions and then jumped straight to regression. ANOVA is just a really specific way of doing a regression. In R, and python::statsmodels you get the answer to (essentially) an ANOVA any time you run an LM or GLM; its the Z-statistic for your whole model. I know there is more nuance to this, but teaching students that they can use regression for most of the problems they would have used seemingly arcane tests for is going to be much more useful for the students. Here is a lovely page demonstrating how to do this in R: https://lindeloev.github.io/tests-as-linear/ https://lindeloev.github.io/tests-as-linear/
- usgroup 3y ago
  I agree with the sentiment although I'm not sure there is the time for all of it. At least when I took them, probability theory and distribution theory were separate semester long courses, and the former was a prerequisite for the latter.
- gpderetta 3y ago
  Stastsmodels and that github page are the only reason I have some understanding of statistical tests.
bunderbunder 3y ago
Principles of Statistics by M.G. Bulmer is a nice introduction to the mathematical side of things. It's part of Dover's classic textbook series, so it's inexpensive compared to newer textbooks, and also concise and well-written. It does assume you already have a solid understanding of calculus and combinatorics, though. Which I think is fair. Discrete statistics is arguably just applied combinatorics, and continuous statistics applied calculus, so if you have a strong foundation in those two subjects then you're already 90% of the way there. (And, if you don't, stop the cart and let the horse catch up.)

ImaCake 3y ago

I think those short courses would be more effective if they didn't bother with ANOVA and instead taught intro probability and distributions and then jumped straight to regression. ANOVA is just a really specific way of doing a regression. In R, and python::statsmodels you get the answer to (essentially) an ANOVA any time you run an LM or GLM; its the Z-statistic for your whole model. I know there is more nuance to this, but teaching students that they can use regression for most of the problems they would have used seemingly arcane tests for is going to be much more useful for the students. Here is a lovely page demonstrating how to do this in R: https://lindeloev.github.io/tests-as-linear/ https://lindeloev.github.io/tests-as-linear/

usgroup 3y ago
I agree with the sentiment although I'm not sure there is the time for all of it. At least when I took them, probability theory and distribution theory were separate semester long courses, and the former was a prerequisite for the latter.
gpderetta 3y ago
Stastsmodels and that github page are the only reason I have some understanding of statistical tests.

bunderbunder 3y ago

Principles of Statistics by M.G. Bulmer is a nice introduction to the mathematical side of things. It's part of Dover's classic textbook series, so it's inexpensive compared to newer textbooks, and also concise and well-written. It does assume you already have a solid understanding of calculus and combinatorics, though. Which I think is fair. Discrete statistics is arguably just applied combinatorics, and continuous statistics applied calculus, so if you have a strong foundation in those two subjects then you're already 90% of the way there. (And, if you don't, stop the cart and let the horse catch up.)