4 ms·

Statistics education is undergoing a bit of a revolution, driven by the accessibility of computers. For example, hypothesis testing is introduced by randomizati

Statistics education is undergoing a bit of a revolution, driven by the accessibility of computers. For example, hypothesis testing is introduced by randomization[1], using a randomized permutation test[2]. I find this really easy to understand, compared to how I learned statistics using a more traditional approach. The traditional approach taught be a cookbook of hypothesis tests to use: use the t-test in this situation, use the chi-squared in this situation, and so on. I never gained any understanding of why I should use these different tests, or where they came from, from the cookbook approach. For the same approach in a slightly different context see [3]. [1]: https://openintro-ims2.netlify.app/11-foundations-randomization https://openintro-ims2.netlify.app/11-foundations-randomizat... [2]: https://en.wikipedia.org/wiki/Permutation_test https://en.wikipedia.org/wiki/Permutation_test [3]: https://inferentialthinking.com/chapters/11/1/Assessing_a_Model.html https://inferentialthinking.com/chapters/11/1/Assessing_a_Mo...

iTokio 3y ago
There is also Brillant that has a very polished interactive course: https://brilliant.org/courses/statistics/ https://brilliant.org/courses/statistics/
- usgroup 3y ago
  These things are great if they add value for you, but I would be very skeptical of any non-mathematical approach to statistics. I think statistics is only made clear by mathematics, much the same as Physics. And one cannot grasp statistics without being able to understand the maths. I think that still the best way to understand statistics is to start with the mathematical theory and to grind 1000+ textbook problems.
  - mkl 3y ago
    > I think that still the best way to understand statistics is to start with the mathematical theory and to grind 1000+ textbook problems. Are there any books you'd recommend for this approach?
    - usgroup 3y ago
      My grind was "Mathematical Statistics with Applications" by Wackerly et al. There are PDF versions if you Google for it. I can't say it was quick, easy or intuitive; but it works. I also liked "In all Likelihood" by Pawitan for a "likelihoodist" foundational approach.
  - jph00 3y ago
    I was introduced to statistics with the mathematical approach, and it failed to help me understand why things were the way they were, due to the lack of context and application. Later I re-learned it in an applied way, and things made much more sense to me. (That's fine if you liked learning it your way, but that's no reason to be skeptical about other approaches.)
usgroup 3y ago
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
dr_dshiv 3y ago
Do you know of any validation studies with Advanced Data Analysis (formerly code interpreter) in chatGPT? I think it can be excellent as a teaching tool.
wespiser_2018 3y ago
The difficulty of teaching statistics is that the maths you need to prove things are right and gain an intuitive understanding of the methods are far more advanced than what is presented in a basic stats course. Gosset came up with the t-test and proved to the world it made sense, yet we teach students to apply it in a black box way without a fundamental understanding of why it's right. That's not great pedagogy. IMO, this is where Bayesian Statistics is far superior. There's a Curry-Howard isomorphism to logic which runs extremely deep, and it's possible to introduce using conjugate distributions with nice closed form analytical solutions. Anything more complex, well, that's what computers are for, and there are great ways (STAN) to run complex distributions that are far more intricate than frequentist methods.
- zozbot234 3y ago
  Maximum likelihood (which underpins many frequentist methods) basically amounts to Bayesian statistics with a uniform prior on your parameters. And the "shape" of your prior actually depends on the chosen parametrization, so in principle you can account for non-flat priors as well.
  - nextos 3y ago
    IMHO, the discussion should not be so much whether to teach Bayesian or maximum likelihood. But instead, whether to teach generative models or to keep going with hypothesis tests, which are generally presented to students as a bag of tricks. Generative models, (implemented in e.g. Stan, PyMC, Pyro, Turing, etc.) split models from inference. So one can switch from maximum likelihood to variational inference or MCMC quite easily. Generative models, beginning from regression, make a lot more sense to students and yield much more robust inference. Most people I know who publish research articles on a frequent basis do not know p-values are not a measure of effect sizes. This demonstrates current education has failed.
  - eutectic 3y ago
    Maximum Likelihood corresponds to Bayesian statistics with MAP estimation, which is not the typical way to use the posterior.
zaptheimpaler 3y ago
Hey i recognized you from the Scala doodle project! that and the other stuff from Underscore was a really cool way to learn Scala & FP, thank you :)
- noelwelsh 3y ago
  That's very random but very cool! I'm glad the books were useful to you :-) This post was actually motivated by my wanting to write some material on data science, wondering what the modern approach to teaching it is, and falling down a rabbit hole.
cbolton 3y ago
I think a common way to teach classical statistics is to start with a binomial test. The binomial distribution is quite concrete so the students can hopefully grasp the concept of p-value. Then things become more abstract with the normal, T distribution, etc. and cookbook of when to use what...

iTokio 3y ago

There is also Brillant that has a very polished interactive course: https://brilliant.org/courses/statistics/ https://brilliant.org/courses/statistics/

usgroup 3y ago
These things are great if they add value for you, but I would be very skeptical of any non-mathematical approach to statistics. I think statistics is only made clear by mathematics, much the same as Physics. And one cannot grasp statistics without being able to understand the maths. I think that still the best way to understand statistics is to start with the mathematical theory and to grind 1000+ textbook problems.
- mkl 3y ago
  > I think that still the best way to understand statistics is to start with the mathematical theory and to grind 1000+ textbook problems. Are there any books you'd recommend for this approach?
  - usgroup 3y ago
    My grind was "Mathematical Statistics with Applications" by Wackerly et al. There are PDF versions if you Google for it. I can't say it was quick, easy or intuitive; but it works. I also liked "In all Likelihood" by Pawitan for a "likelihoodist" foundational approach.
- jph00 3y ago
  I was introduced to statistics with the mathematical approach, and it failed to help me understand why things were the way they were, due to the lack of context and application. Later I re-learned it in an applied way, and things made much more sense to me. (That's fine if you liked learning it your way, but that's no reason to be skeptical about other approaches.)

usgroup 3y ago

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

dr_dshiv 3y ago

Do you know of any validation studies with Advanced Data Analysis (formerly code interpreter) in chatGPT? I think it can be excellent as a teaching tool.

wespiser_2018 3y ago

The difficulty of teaching statistics is that the maths you need to prove things are right and gain an intuitive understanding of the methods are far more advanced than what is presented in a basic stats course. Gosset came up with the t-test and proved to the world it made sense, yet we teach students to apply it in a black box way without a fundamental understanding of why it's right. That's not great pedagogy. IMO, this is where Bayesian Statistics is far superior. There's a Curry-Howard isomorphism to logic which runs extremely deep, and it's possible to introduce using conjugate distributions with nice closed form analytical solutions. Anything more complex, well, that's what computers are for, and there are great ways (STAN) to run complex distributions that are far more intricate than frequentist methods.

zozbot234 3y ago
Maximum likelihood (which underpins many frequentist methods) basically amounts to Bayesian statistics with a uniform prior on your parameters. And the "shape" of your prior actually depends on the chosen parametrization, so in principle you can account for non-flat priors as well.
- nextos 3y ago
  IMHO, the discussion should not be so much whether to teach Bayesian or maximum likelihood. But instead, whether to teach generative models or to keep going with hypothesis tests, which are generally presented to students as a bag of tricks. Generative models, (implemented in e.g. Stan, PyMC, Pyro, Turing, etc.) split models from inference. So one can switch from maximum likelihood to variational inference or MCMC quite easily. Generative models, beginning from regression, make a lot more sense to students and yield much more robust inference. Most people I know who publish research articles on a frequent basis do not know p-values are not a measure of effect sizes. This demonstrates current education has failed.
- eutectic 3y ago
  Maximum Likelihood corresponds to Bayesian statistics with MAP estimation, which is not the typical way to use the posterior.

zaptheimpaler 3y ago

Hey i recognized you from the Scala doodle project! that and the other stuff from Underscore was a really cool way to learn Scala & FP, thank you :)

noelwelsh 3y ago
That's very random but very cool! I'm glad the books were useful to you :-) This post was actually motivated by my wanting to write some material on data science, wondering what the modern approach to teaching it is, and falling down a rabbit hole.

cbolton 3y ago

I think a common way to teach classical statistics is to start with a binomial test. The binomial distribution is quite concrete so the students can hopefully grasp the concept of p-value. Then things become more abstract with the normal, T distribution, etc. and cookbook of when to use what...