11 ms·

Introduction to Modern Statistics

740 points by noelwelsh 3y ago

noelwelsh 3y ago
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...
jna_sh 3y ago
Very excited to see Mine Çetinkaya-Rundel is an author here! Many might be familiar with “R for Data Science” (https://r4ds.had.co.nz/ https://r4ds.had.co.nz/), to which she is a contributor, but she’s also published a lot of great papers around teaching data science.
- ayhanfuat 3y ago
  She also has some online courses on Coursera (https://www.coursera.org/instructor/minecetinkayarundel https://www.coursera.org/instructor/minecetinkayarundel). Hands down one of the best instructors I have seen.
zvmaz 3y ago
What is a good book on statistics that one can use for self-learning?
- noelwelsh 3y ago
  Depends where you are starting from and what you want to learn. The linked book is a first year introduction, and does a good job of that. If you want to go further there are many other options: * Statistical Inference by Casella and Berger. This book has a very good reputation for building statistics from first principles. I won't link to them, but you can find full PDF scans online with a simple search. Amazon reviews: https://www.amazon.com/Statistical-Inference-Roger-Berger/dp/0534243126 https://www.amazon.com/Statistical-Inference-Roger-Berger/dp... * Statistics by Freedman, Pisani, and Purves has similarly very good reviews and can be easily found online. Amazon reviews: https://www.amazon.com/Statistics-Fourth-David-Freedman-ebook/dp/B00SLB5Q72 https://www.amazon.com/Statistics-Fourth-David-Freedman-eboo... * The majority of the Berkeley data science core curriculum books are online. This is not purely statistics but 1) is taught in a modern style that makes use of computation and randomization and 2) uses tools that may be useful to learn about. 1. https://inferentialthinking.com/chapters/intro.html https://inferentialthinking.com/chapters/intro.html (Data 8) 2. https://learningds.org/intro.html https://learningds.org/intro.html (Data 100) 3. http://prob140.org/textbook/content/README.html http://prob140.org/textbook/content/README.html (Data 140) 4. https://data102.org/fa23/resources/#textbooks-from-previous-data-science-courses https://data102.org/fa23/resources/#textbooks-from-previous-... (Data 102; this gets into machine learning and pure statistics) The Berkeley curriculum is not the only one; there are tens, possibly hundreds, of online courses. The Berkeley curriculum is just 1) quite extensive and 2) the one I happened to read the most about when I was recently researching how data science is currently taught.
- sudoankit 3y ago
  I particularly like Statistical Inference by George Casella and Roger Lee Berger. You could also look at Introduction to Probability by Joseph K. Blitzstein and Jessica Hwang (available for free here: http://probabilitybook.net http://probabilitybook.net (redirects to drive)).
ricksunny 3y ago
I'm looking for help with distilling 'truth' from folk belief systems by formalizng them under a Bayesian network framework, in case anyone is looking for a project through which to sharpen their statistical saw.
d00mer 3y ago
They should remove "modern" from the title, because who the hell uses the "R programming language" these days anymore?
- Onawa 3y ago
  Everyone in my branch of Toxicology? Tons of people in biological sciences. Just because you have bias against the tool and don't run in the same circles doesn't mean that R isn't used and love by a subset of devs.
- noelwelsh 3y ago
  Statisticians do. The Berkeley curriculum, which I've linked to in another comment, uses Python.
- adr1an 3y ago
  Everyone but you. Check any statistics journal. Only a few people developing methods switched to Python or Julia.
- i_love_limes 3y ago
  A lot of people... in fact a huge portion of statisticians, epidemiologists, econometrics, use it as their primary language. I do genetic epidemiology (which is considerably more compute intensive than regular epidemiology), and R is still the most common language, with the most libraries and packages being used for it, compared to python for example. I think maybe you should consider being less forthcoming with your opinions on topics which you are not well informed on.
  - wespiser_2018 3y ago
    I worked in data science for a few start ups, and even though I know Python (it's my LeetCode language of choice), R just dominates when it comes to accessing academic methods and computational analysis. If you are going to push the boundaries of what you can and can't analysis for statistical effects and leverage academic learnings, it's R.
- dereify 3y ago
dleeftink 3y ago
Anyone looking to apply and compare frequentist and bayesian methods within a unified GUI (which is essentially an elegant wrapper to R and selected/custom statistical packages), should check out JASP developed by the University of Amsterdam [0]. It's free to use, and the graphs + captions generated during each step are publication quality right out of the box. Using it truly feels like a 'fresh way' to do statistics. Its main website provides ample use cases, guides and tutorials, and I often return to the blog for the well documented deepdives into how traditional frequentist methods and their bayesian counterparts compare (the animated explainers are especially helpful, and I appreciate the devs reflecting on each release and future directions). [0]: https://jasp-stats.org/ https://jasp-stats.org/
- NeutralForest 3y ago
  there was an interview of one of the JASP (creator or maintainer, can't remember) in the "Learn Bayesian Stats" podcast; it was very interesting.
  - rdhyee 3y ago
    I think the referenced episode is https://learnbayesstats.com/episode/61-why-we-still-use-non-bayesian-methods-ej-wagenmakers/ https://learnbayesstats.com/episode/61-why-we-still-use-non-... Thanks for pointing it out!
  - dleeftink 3y ago
    To me, it's academic software done right, both in terms of accessibility and maintenance. I'd love to hear more about their governance and funding structure and how this might be applied elsewhere, and learn about academic software of similar grade and utility.
- mindcrime 3y ago
  Even better than just being "free to use" it's F/OSS (under the AGPL): https://github.com/jasp-stats/jasp-desktop https://github.com/jasp-stats/jasp-desktop
- 3abiton 3y ago
begemotz 3y ago
I like the inclusion of randomization and bootstrapping. It's unfortunate that the hypothesis framework is still NHST -- I wouldn't consider that 'modern' by any means.
- noelwelsh 3y ago
  I don't see widespread agreement in the statistics community as to what should replace NHST. If you go Bayesian you need to completely rewrite the course. I've seen confidence intervals suggested as an alternative, but there are arguments against. I've also seen arguments that hypothesis tests shouldn't be used at all. Given that NHST is still widely used and there isn't a clear alternative I think it's a disservice to students to not introduce them.
  - begemotz 3y ago
    I probably should have been more clear. I didn't say hypothesis testing, I said NHST (the binary null/alt hypothesis approach) - which is an approach to hypothesis testing particularly prevelant in certain disciplines such as Psychology. And in that context, there is a lot of agreement that this approach is fundamentally flawed and outdated. if you are interested, I can provide references when I get to the office. But off the top of my head consider Gigerenzer and Cummings.
    - noelwelsh 3y ago
      For those following along at home Gigerenzer is, I think, "Mindless Statistics"[1] and Cummings is "The New Statistics"[2]. [1]: https://pure.mpg.de/rest/items/item_2101336/component/file_2101335/content https://pure.mpg.de/rest/items/item_2101336/component/file_2... [2]: Sample at https://tandfbis.s3.amazonaws.com/rt-media/pp/common/sample-chapters/9780415879682.pdf https://tandfbis.s3.amazonaws.com/rt-media/pp/common/sample-...
      - begemotz 3y ago
        Yes, those are appropriate (although Gigerenzer and Cummings both have other relevant publications on the topic). As for a undergraduate text that 'teaches the difference', you can look at 'An Introduction to Statistics' by Carlson & Winquist.
RedShift1 3y ago
Can I download this as a PDF? I'd like to read it offline.
- noelwelsh 3y ago
  Here: https://www.openintro.org/book/ims/ https://www.openintro.org/book/ims/
  - RedShift1 3y ago
    This is the first version, not the 2nd?
    - noelwelsh 3y ago
      Hmmm ... must be because the 2nd edition is still in progress. Best option might be to follow the immortal words of Obiwan Kenobi and "use the source": https://github.com/OpenIntroStat/ims https://github.com/OpenIntroStat/ims Otherwise you can try building a PDF from the very similar Data 8 book[1] using [2] [1]: https://github.com/data-8/textbook https://github.com/data-8/textbook [2]: https://jupyterbook.org/en/stable/advanced/pdf.html https://jupyterbook.org/en/stable/advanced/pdf.html
usgroup 3y ago
I think Ronald Fisher may not have used bootstrap to calculate confidence intervals; but it looks to me like he invented most of the rest of the syllabus .. in the early 1900s :-)
mjburgess 3y ago
What's often missing from these introductions is when statistics will not work; and what it even means when it "works". The amount of data needed to tell between two normal is about 30 data points -- between two power-law distributions, >trillion. (And this basically scuppers the central limit theorem, on which a lot of cargo-cult stats is justified). Stats, imv, should be taught simulation-first: code up your hypotheses and see if they're even testable. Many many projects would immediately fail at the research stage. Next, know that predictions are almost never a good goal. Almost everything is practically unpredictable -- with a near infinite number of relevant causes, uncontrollable. At best, in ideal cases, you can use stats to model a distribution of predictions and then determine a risk/value across that range. Ie., the goal isnt to predict anything but to prescribe some action (or inference) according to a risk tolerance (risk of error, or financial risk, etc.). It seems a generation of people have half-learned bits of stats, glued them together, and created widespread 'statistical cargo-cultism'. The lesson of stats isnt hypothesis testing, but how almost no hypotheses are testable -- and then what do you do
- Ensorceled 3y ago
  It's ironic that this ... rant? ... is basically unreadable without knowledge of basic statistical methods. How do you teach any of this to someone who hasn't already taken introductory statistics? How do you learn anything if you first have to learn the myriad ways something you don't even have a basic working knowledge of can fail before you learn it?
  - mjburgess 3y ago
    The comment is addressed to the informed reader who is the only one with a hope of being persuaded on this point. To teach this, from scratch, I think is fairly easy -- but there's few with any incentive to do it. Many in academia wouldnt know how, and if they did, would discover that much of their research can be shown a priori to not be worthwhile (rather than after a decade of 'debate'). All you really need is to start with establishing an intuitive understanding of randomness, how apparently highly patterned it is, and so on. Then ask: how easy is it to reproduce an observed pattern with (simulated) randomness? That question alone, properly supported via basic programming simulations, will take you extremely far. Indeed, the answer to it is often obvious -- a trivial program. That few ever write such programs shows how the whole edifice of stats education is geared towards confirmation bias. Before computers, stats was either an extremely mathematical disipline seeking (empirically useless) formula for toy models; or using heuristic empirical formula that rarely applied. Computers basically obviate all of that. Stats is mostly about counting things and making comparisons -- perfect tasks for machines. with only a few high-school mathematical formula most could derive most useful statistical techniques as simple computer programs.
elashri 3y ago
Thanks to the author for the book and making it open access. I always admire these efforts.
Andrew018 3y ago
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growingkittens 3y ago
Is there a "pre-statistics" book that teaches the thinking skills and concepts needed to understand statistics?
- ndr 3y ago
  This book seems to start where you need it to start. You don't need much beyond basic calculus. Most suffer from some mental block they got installed at a young age akin those that say "I'm bad at math" because their teacher sucked. Dive in and you won't regret it.
  - obscurette 3y ago
    I have been a math teacher and although I can't guarantee that I didn't suck, I can say that most of kids don't develop this attitude because of teachers, but because of their parents. "My mum says that she sucked at math/music/whatever as well, so do I!" is far too common. As a teacher I just didn't have resources to influence this attitude either.
    - ndr 3y ago
      Yes, parents can be horrible too. Unfortunately it's somehow socially acceptable and even worthy of pride in some circles, to be "bad at math". It's seems very rare for someone to openly say "I'm bad at [my native language]" or "writing". I feel stats is has a somewhat similar effect even among those with math education. Several friends who have a degree in math recoil at the first mention of stats concepts.
      - obscurette 3y ago
        > It's seems very rare for someone to openly say "I'm bad at [my native language]" or "writing". It is actually even fashionable in non-english countries. Declaring "I'm bad at [my native language], I only use english anyway" makes you a better person somehow. And it's not rare in other areas either – in post-truth world it's trendy not to know things.
armcat 3y ago
One of my favourite books on statistics and probability is "Regression and Other Stories", by Andrew Gelman, Jennifer Hill and Aki Vehtari. You can access the book for free here: https://users.aalto.fi/~ave/ROS.pdf https://users.aalto.fi/~ave/ROS.pdf
- epgui 3y ago
  +1, this is a great textbook, and not just for social sciences as the second header would suggest.
epgui 3y ago
As much as I appreciate and love all pedagogical endeavours in the field, especially in the form of open texts, I really, really, really dislike this overall approach to teaching introductory statistics. I'm hoping to see, over time, a shift away from ad-hoc null hypothesis testing in favour of linear models (yes, in introductory courses, from the start-- see link below) and Bayesian-by-default approaches. https://lindeloev.github.io/tests-as-linear/#:~:text=Most%20of%20the%20common%20statistical,most%20students%20know%20from%20highschool https://lindeloev.github.io/tests-as-linear/#:~:text=Most%20....
- bschne 3y ago
  I am partway through McElreath's "Statistical Rethinking" and I fully agree with this.
  - epgui 3y ago
    That's a great textbook!
    - deleted 3y ago
      [deleted]
    - TheAlchemist 3y ago
      It's been recommended on this topic several times, so I'm looking at it. Quite expensive ! I see there is a series of lectures, which seems identical to the book. Is it the same ? Or still worth buying the book ?
      - noelwelsh 3y ago
        The lectures are good, and I've been told the book can be found online by the intrepid. I guess that Anna's Archive or Library Genesis has it.
        TheAlchemist 3y ago
        I've found the book indeed - although it seems to be the first edition. It's here: https://civil.colorado.edu/~balajir/CVEN6833/bayes-resources/RM-StatRethink-Bayes.pdf https://civil.colorado.edu/~balajir/CVEN6833/bayes-resources...
deleted 3y ago
[deleted]
willsmith72 3y ago
The epub is apparently too big to send to a kindle, but I can't see the option to download it, only the pdf. Any ideas?
- LemonSodaPop 3y ago
  Too big to email? I use calibre to convert any file-type i have and send it directly to my kindle.
  - willsmith72 3y ago
    me too, but the epub -> pdf conversion is never perfect in my experience, with random headers through the text or weird paragraph splits. The too big error was from openintro.com, where they have a "send to kindle" option which I was hoping was a proper epub
tea-coffee 3y ago
This looks to be the 2nd edition. Can anyone comment on how the 1st edition was?
mavam 3y ago
For studying statistics, I put together a comprehensive cheat sheet: https://github.com/mavam/stat-cookbook https://github.com/mavam/stat-cookbook
mdaniel 3y ago
Seems to be mostly Creative Commons BY-SA 3.0 but there's a lot of "yes, but" language in that file: https://github.com/OpenIntroStat/ims/blob/main/LICENSE.md https://github.com/OpenIntroStat/ims/blob/main/LICENSE.md

740 points by noelwelsh 3y ago

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...

jna_sh 3y ago

Very excited to see Mine Çetinkaya-Rundel is an author here! Many might be familiar with “R for Data Science” (https://r4ds.had.co.nz/ https://r4ds.had.co.nz/), to which she is a contributor, but she’s also published a lot of great papers around teaching data science.

ayhanfuat 3y ago
She also has some online courses on Coursera (https://www.coursera.org/instructor/minecetinkayarundel https://www.coursera.org/instructor/minecetinkayarundel). Hands down one of the best instructors I have seen.

zvmaz 3y ago

What is a good book on statistics that one can use for self-learning?

noelwelsh 3y ago
Depends where you are starting from and what you want to learn. The linked book is a first year introduction, and does a good job of that. If you want to go further there are many other options: * Statistical Inference by Casella and Berger. This book has a very good reputation for building statistics from first principles. I won't link to them, but you can find full PDF scans online with a simple search. Amazon reviews: https://www.amazon.com/Statistical-Inference-Roger-Berger/dp/0534243126 https://www.amazon.com/Statistical-Inference-Roger-Berger/dp... * Statistics by Freedman, Pisani, and Purves has similarly very good reviews and can be easily found online. Amazon reviews: https://www.amazon.com/Statistics-Fourth-David-Freedman-ebook/dp/B00SLB5Q72 https://www.amazon.com/Statistics-Fourth-David-Freedman-eboo... * The majority of the Berkeley data science core curriculum books are online. This is not purely statistics but 1) is taught in a modern style that makes use of computation and randomization and 2) uses tools that may be useful to learn about. 1. https://inferentialthinking.com/chapters/intro.html https://inferentialthinking.com/chapters/intro.html (Data 8) 2. https://learningds.org/intro.html https://learningds.org/intro.html (Data 100) 3. http://prob140.org/textbook/content/README.html http://prob140.org/textbook/content/README.html (Data 140) 4. https://data102.org/fa23/resources/#textbooks-from-previous-data-science-courses https://data102.org/fa23/resources/#textbooks-from-previous-... (Data 102; this gets into machine learning and pure statistics) The Berkeley curriculum is not the only one; there are tens, possibly hundreds, of online courses. The Berkeley curriculum is just 1) quite extensive and 2) the one I happened to read the most about when I was recently researching how data science is currently taught.
sudoankit 3y ago
I particularly like Statistical Inference by George Casella and Roger Lee Berger. You could also look at Introduction to Probability by Joseph K. Blitzstein and Jessica Hwang (available for free here: http://probabilitybook.net http://probabilitybook.net (redirects to drive)).

ricksunny 3y ago

I'm looking for help with distilling 'truth' from folk belief systems by formalizng them under a Bayesian network framework, in case anyone is looking for a project through which to sharpen their statistical saw.

d00mer 3y ago

They should remove "modern" from the title, because who the hell uses the "R programming language" these days anymore?

Onawa 3y ago
Everyone in my branch of Toxicology? Tons of people in biological sciences. Just because you have bias against the tool and don't run in the same circles doesn't mean that R isn't used and love by a subset of devs.
noelwelsh 3y ago
Statisticians do. The Berkeley curriculum, which I've linked to in another comment, uses Python.
adr1an 3y ago
Everyone but you. Check any statistics journal. Only a few people developing methods switched to Python or Julia.
i_love_limes 3y ago
A lot of people... in fact a huge portion of statisticians, epidemiologists, econometrics, use it as their primary language. I do genetic epidemiology (which is considerably more compute intensive than regular epidemiology), and R is still the most common language, with the most libraries and packages being used for it, compared to python for example. I think maybe you should consider being less forthcoming with your opinions on topics which you are not well informed on.
- wespiser_2018 3y ago
  I worked in data science for a few start ups, and even though I know Python (it's my LeetCode language of choice), R just dominates when it comes to accessing academic methods and computational analysis. If you are going to push the boundaries of what you can and can't analysis for statistical effects and leverage academic learnings, it's R.
dereify 3y ago

dleeftink 3y ago

Anyone looking to apply and compare frequentist and bayesian methods within a unified GUI (which is essentially an elegant wrapper to R and selected/custom statistical packages), should check out JASP developed by the University of Amsterdam [0]. It's free to use, and the graphs + captions generated during each step are publication quality right out of the box. Using it truly feels like a 'fresh way' to do statistics. Its main website provides ample use cases, guides and tutorials, and I often return to the blog for the well documented deepdives into how traditional frequentist methods and their bayesian counterparts compare (the animated explainers are especially helpful, and I appreciate the devs reflecting on each release and future directions). [0]: https://jasp-stats.org/ https://jasp-stats.org/

NeutralForest 3y ago
there was an interview of one of the JASP (creator or maintainer, can't remember) in the "Learn Bayesian Stats" podcast; it was very interesting.
- rdhyee 3y ago
  I think the referenced episode is https://learnbayesstats.com/episode/61-why-we-still-use-non-bayesian-methods-ej-wagenmakers/ https://learnbayesstats.com/episode/61-why-we-still-use-non-... Thanks for pointing it out!
- dleeftink 3y ago
  To me, it's academic software done right, both in terms of accessibility and maintenance. I'd love to hear more about their governance and funding structure and how this might be applied elsewhere, and learn about academic software of similar grade and utility.
mindcrime 3y ago
Even better than just being "free to use" it's F/OSS (under the AGPL): https://github.com/jasp-stats/jasp-desktop https://github.com/jasp-stats/jasp-desktop
3abiton 3y ago

begemotz 3y ago

I like the inclusion of randomization and bootstrapping. It's unfortunate that the hypothesis framework is still NHST -- I wouldn't consider that 'modern' by any means.

noelwelsh 3y ago
I don't see widespread agreement in the statistics community as to what should replace NHST. If you go Bayesian you need to completely rewrite the course. I've seen confidence intervals suggested as an alternative, but there are arguments against. I've also seen arguments that hypothesis tests shouldn't be used at all. Given that NHST is still widely used and there isn't a clear alternative I think it's a disservice to students to not introduce them.
- begemotz 3y ago
  I probably should have been more clear. I didn't say hypothesis testing, I said NHST (the binary null/alt hypothesis approach) - which is an approach to hypothesis testing particularly prevelant in certain disciplines such as Psychology. And in that context, there is a lot of agreement that this approach is fundamentally flawed and outdated. if you are interested, I can provide references when I get to the office. But off the top of my head consider Gigerenzer and Cummings.
  - noelwelsh 3y ago
    For those following along at home Gigerenzer is, I think, "Mindless Statistics"[1] and Cummings is "The New Statistics"[2]. [1]: https://pure.mpg.de/rest/items/item_2101336/component/file_2101335/content https://pure.mpg.de/rest/items/item_2101336/component/file_2... [2]: Sample at https://tandfbis.s3.amazonaws.com/rt-media/pp/common/sample-chapters/9780415879682.pdf https://tandfbis.s3.amazonaws.com/rt-media/pp/common/sample-...
    - begemotz 3y ago
      Yes, those are appropriate (although Gigerenzer and Cummings both have other relevant publications on the topic). As for a undergraduate text that 'teaches the difference', you can look at 'An Introduction to Statistics' by Carlson & Winquist.

RedShift1 3y ago

Can I download this as a PDF? I'd like to read it offline.

noelwelsh 3y ago
Here: https://www.openintro.org/book/ims/ https://www.openintro.org/book/ims/
- RedShift1 3y ago
  This is the first version, not the 2nd?
  - noelwelsh 3y ago
    Hmmm ... must be because the 2nd edition is still in progress. Best option might be to follow the immortal words of Obiwan Kenobi and "use the source": https://github.com/OpenIntroStat/ims https://github.com/OpenIntroStat/ims Otherwise you can try building a PDF from the very similar Data 8 book[1] using [2] [1]: https://github.com/data-8/textbook https://github.com/data-8/textbook [2]: https://jupyterbook.org/en/stable/advanced/pdf.html https://jupyterbook.org/en/stable/advanced/pdf.html

usgroup 3y ago

I think Ronald Fisher may not have used bootstrap to calculate confidence intervals; but it looks to me like he invented most of the rest of the syllabus .. in the early 1900s :-)

mjburgess 3y ago

What's often missing from these introductions is when statistics will not work; and what it even means when it "works". The amount of data needed to tell between two normal is about 30 data points -- between two power-law distributions, >trillion. (And this basically scuppers the central limit theorem, on which a lot of cargo-cult stats is justified). Stats, imv, should be taught simulation-first: code up your hypotheses and see if they're even testable. Many many projects would immediately fail at the research stage. Next, know that predictions are almost never a good goal. Almost everything is practically unpredictable -- with a near infinite number of relevant causes, uncontrollable. At best, in ideal cases, you can use stats to model a distribution of predictions and then determine a risk/value across that range. Ie., the goal isnt to predict anything but to prescribe some action (or inference) according to a risk tolerance (risk of error, or financial risk, etc.). It seems a generation of people have half-learned bits of stats, glued them together, and created widespread 'statistical cargo-cultism'. The lesson of stats isnt hypothesis testing, but how almost no hypotheses are testable -- and then what do you do

Ensorceled 3y ago
It's ironic that this ... rant? ... is basically unreadable without knowledge of basic statistical methods. How do you teach any of this to someone who hasn't already taken introductory statistics? How do you learn anything if you first have to learn the myriad ways something you don't even have a basic working knowledge of can fail before you learn it?
- mjburgess 3y ago
  The comment is addressed to the informed reader who is the only one with a hope of being persuaded on this point. To teach this, from scratch, I think is fairly easy -- but there's few with any incentive to do it. Many in academia wouldnt know how, and if they did, would discover that much of their research can be shown a priori to not be worthwhile (rather than after a decade of 'debate'). All you really need is to start with establishing an intuitive understanding of randomness, how apparently highly patterned it is, and so on. Then ask: how easy is it to reproduce an observed pattern with (simulated) randomness? That question alone, properly supported via basic programming simulations, will take you extremely far. Indeed, the answer to it is often obvious -- a trivial program. That few ever write such programs shows how the whole edifice of stats education is geared towards confirmation bias. Before computers, stats was either an extremely mathematical disipline seeking (empirically useless) formula for toy models; or using heuristic empirical formula that rarely applied. Computers basically obviate all of that. Stats is mostly about counting things and making comparisons -- perfect tasks for machines. with only a few high-school mathematical formula most could derive most useful statistical techniques as simple computer programs.

elashri 3y ago

Thanks to the author for the book and making it open access. I always admire these efforts.

Andrew018 3y ago

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growingkittens 3y ago

Is there a "pre-statistics" book that teaches the thinking skills and concepts needed to understand statistics?

ndr 3y ago
This book seems to start where you need it to start. You don't need much beyond basic calculus. Most suffer from some mental block they got installed at a young age akin those that say "I'm bad at math" because their teacher sucked. Dive in and you won't regret it.
- obscurette 3y ago
  I have been a math teacher and although I can't guarantee that I didn't suck, I can say that most of kids don't develop this attitude because of teachers, but because of their parents. "My mum says that she sucked at math/music/whatever as well, so do I!" is far too common. As a teacher I just didn't have resources to influence this attitude either.
  - ndr 3y ago
    Yes, parents can be horrible too. Unfortunately it's somehow socially acceptable and even worthy of pride in some circles, to be "bad at math". It's seems very rare for someone to openly say "I'm bad at [my native language]" or "writing". I feel stats is has a somewhat similar effect even among those with math education. Several friends who have a degree in math recoil at the first mention of stats concepts.
    - obscurette 3y ago
      > It's seems very rare for someone to openly say "I'm bad at [my native language]" or "writing". It is actually even fashionable in non-english countries. Declaring "I'm bad at [my native language], I only use english anyway" makes you a better person somehow. And it's not rare in other areas either – in post-truth world it's trendy not to know things.

armcat 3y ago

One of my favourite books on statistics and probability is "Regression and Other Stories", by Andrew Gelman, Jennifer Hill and Aki Vehtari. You can access the book for free here: https://users.aalto.fi/~ave/ROS.pdf https://users.aalto.fi/~ave/ROS.pdf

epgui 3y ago
+1, this is a great textbook, and not just for social sciences as the second header would suggest.

epgui 3y ago

As much as I appreciate and love all pedagogical endeavours in the field, especially in the form of open texts, I really, really, really dislike this overall approach to teaching introductory statistics. I'm hoping to see, over time, a shift away from ad-hoc null hypothesis testing in favour of linear models (yes, in introductory courses, from the start-- see link below) and Bayesian-by-default approaches. https://lindeloev.github.io/tests-as-linear/#:~:text=Most%20of%20the%20common%20statistical,most%20students%20know%20from%20highschool https://lindeloev.github.io/tests-as-linear/#:~:text=Most%20....

bschne 3y ago
I am partway through McElreath's "Statistical Rethinking" and I fully agree with this.
- epgui 3y ago
  That's a great textbook!
  - deleted 3y ago
    [deleted]
  - TheAlchemist 3y ago
    It's been recommended on this topic several times, so I'm looking at it. Quite expensive ! I see there is a series of lectures, which seems identical to the book. Is it the same ? Or still worth buying the book ?
    - noelwelsh 3y ago
      The lectures are good, and I've been told the book can be found online by the intrepid. I guess that Anna's Archive or Library Genesis has it.
      - TheAlchemist 3y ago
        I've found the book indeed - although it seems to be the first edition. It's here: https://civil.colorado.edu/~balajir/CVEN6833/bayes-resources/RM-StatRethink-Bayes.pdf https://civil.colorado.edu/~balajir/CVEN6833/bayes-resources...

deleted 3y ago

[deleted]

willsmith72 3y ago

The epub is apparently too big to send to a kindle, but I can't see the option to download it, only the pdf. Any ideas?

LemonSodaPop 3y ago
Too big to email? I use calibre to convert any file-type i have and send it directly to my kindle.
- willsmith72 3y ago
  me too, but the epub -> pdf conversion is never perfect in my experience, with random headers through the text or weird paragraph splits. The too big error was from openintro.com, where they have a "send to kindle" option which I was hoping was a proper epub

tea-coffee 3y ago

This looks to be the 2nd edition. Can anyone comment on how the 1st edition was?

mavam 3y ago

For studying statistics, I put together a comprehensive cheat sheet: https://github.com/mavam/stat-cookbook https://github.com/mavam/stat-cookbook

mdaniel 3y ago

Seems to be mostly Creative Commons BY-SA 3.0 but there's a lot of "yes, but" language in that file: https://github.com/OpenIntroStat/ims/blob/main/LICENSE.md https://github.com/OpenIntroStat/ims/blob/main/LICENSE.md