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This is such a great story, it should be included in every intro stats class (I did, back when I taught intro stats). Gosset didn’t have the mathematical backg

This is such a great story, it should be included in every intro stats class (I did, back when I taught intro stats). Gosset didn’t have the mathematical background to derive the correct distribution theoretically, so he figured out what it was by simulating drawing samples of different sizes thousands of times and fitting curves. Simulating, in those days, meant writing numbers on thousands of cards, then shuffling and drawing a sample. Calculate the mean and standard deviation. Repeat. Thousands of times. He published the result with an apologetic shrug for not being able to prove it properly.

richrichie 2y ago
along with compulsory Guinness tasting :)
ForOldHack 2y ago
Um. Wow. That's quite a story. But, it's not real. "owever, Guinness had a policy of not publishing company data, and allowed Gosset to publish his observations on the strict understanding that he did so anonymously." I'm 1906, Gosset was the guest of Person at UCL, and since Gosset had a First in Math, and Professor Pearson was the leading mathematician and publisher of the Bell curve.. Gosset spent a year at UCL. University College London. A year with an expert looking over his shoulder? I would think that he would publish with an extreme amount of confidence, forgoing the need for an apolocetic shrug, which I have never ever heard of. Never, and I have a degree in math with a minor in Statistics. They had playing cards. You are arguing for large sample sizes, which is not economical - precisely against the design of the test - which looks surprisingly suspicious.
- zinekeller 2y ago
  > But, it's not real. "owever, Guinness had a policy of not publishing company data, and allowed Gosset to publish his observations on the strict understanding that he did so anonymously." Except that this part is true. Obviously, he is well-known in academic circles, but Guinness did have a policy against its employees to publish their research using a pseudonym[1]. [1] Specifically, they can publish with three conditions: 1) To not mention Guinness or its competitors, 2) To not mention anything about beer (so topics specifically about beer is forbidden), and 3) To not publish using their surname (which in practical effect is to publish using a pseudonym).
- CrazyStat 2y ago
  > I would think that he would publish with an extreme amount of confidence, forgoing the need for an apolocetic shrug, which I have never ever heard of. Never, and I have a degree in math with a minor in Statistics. Good for you. As you might have guessed from reading that I used to teach statistics, I have a bit more than a minor in the subject. Your attempt to appeal to authority, not to put too fine a point on it, falls flat. Just because you haven’t heard of a thing don’t mean it isn’t true. We can, after all, just read the original paper: > Before I had succeeded in solving my problem analytically, I had endeavoured to do so empirically. The material used was a correlation table containing the height and left middle finger measurements of 3000 criminals, from a paper by W. R. Macdonnell (Biometrika, i, p. 219). The measurements were written out on 3000 pieces of cardboard, which were then very thoroughly shuffled and drawn at random. As each card was drawn its numbers were written down in a book, which thus contains the measurements of 3000 criminals in a random order. Finally, each consecutive set of 4 was taken as a sample—750 in all—and the mean, standard deviation, and correlation5 of each sample determined. The difference between the mean of each sample and the mean of the population was then divided by the standard deviation of the sample, giving us the z of Section III. As for the apologetic shrug, in the course of the “analytic solution” we have: > The law of formation of these moment coefficients appears to be a simple one, but I have not seen my way to a general proof. and then after a bit more math guessing the correct distribution based on the moments > Consequently a curve of Prof. Pearson’s Type III may he expected to fit the distribution of s2. My story is slightly off; Gosset only used one sample size rather than several different sample sizes. But he did use simulation with thousands of hand written cards as his approach to the problem, he did fail to prove the correct distribution (moments are not sufficient to determine the distribution), and he did publish with an apologetic shrug.
- jll29 2y ago
  Typo: guest of Person => Karl Pearson
0xDEAFBEAD 2y ago
It's interesting how mathematically shallow most stats presentations are. In most other areas I've studied, you start from some basics like axioms and gradually build up machinery by proving theorems etc. But presentations I've seen of the t-test focus on when and how to use it, without going very deep into the derivation at all. This leaves me skeptical of the movement to replace calculus with stats in high school. It's true that an ordinary citizen will find stats more useful. But for students who will go on to become scientists and engineers, I think they should study calculus. Calculus is a better on-ramp to the sort of rigor you need in upper-level math. And I'm concerned that a bad "cargo cult" stats class may be worse than no stats education at all. Calculus education seems harder to screw up.
- blt 2y ago
  Not sure why you are downvoted for this. Your points have merit. I agree that stats classes can have a "cookbook" flavor and do not generally lead to a deep understanding of probability. But I would rather fix the stats classes than abandon the topic. Does anyone really argue to replace calculus with stats? I thought the idea was to offer both and let students choose based on their interests.
  - jll29 2y ago
    Propbabilities, combinatorics, logics and sets are the most valuable things from high school maths that benefitted me all the way through from teenager to professor. Calculus is intellectually stimulating, but for my line of work (dealing with uncertaintly, risk, decision making, AI), other parts of mathematics are more useful. However, I would not argue calculus should be replaced. I would argue for more "proper" maths to replace "recipe-like" maths. It's more important to go deeper on a topic than what the topic is.
    - CrazyStat 2y ago
      Combinatorics would make a great high school math course, honestly. Lots of fun puzzles and very approachable.
    - 2y ago

richrichie 2y ago

along with compulsory Guinness tasting :)

ForOldHack 2y ago

Um. Wow. That's quite a story. But, it's not real. "owever, Guinness had a policy of not publishing company data, and allowed Gosset to publish his observations on the strict understanding that he did so anonymously." I'm 1906, Gosset was the guest of Person at UCL, and since Gosset had a First in Math, and Professor Pearson was the leading mathematician and publisher of the Bell curve.. Gosset spent a year at UCL. University College London. A year with an expert looking over his shoulder? I would think that he would publish with an extreme amount of confidence, forgoing the need for an apolocetic shrug, which I have never ever heard of. Never, and I have a degree in math with a minor in Statistics. They had playing cards. You are arguing for large sample sizes, which is not economical - precisely against the design of the test - which looks surprisingly suspicious.

zinekeller 2y ago
> But, it's not real. "owever, Guinness had a policy of not publishing company data, and allowed Gosset to publish his observations on the strict understanding that he did so anonymously." Except that this part is true. Obviously, he is well-known in academic circles, but Guinness did have a policy against its employees to publish their research using a pseudonym[1]. [1] Specifically, they can publish with three conditions: 1) To not mention Guinness or its competitors, 2) To not mention anything about beer (so topics specifically about beer is forbidden), and 3) To not publish using their surname (which in practical effect is to publish using a pseudonym).
CrazyStat 2y ago
> I would think that he would publish with an extreme amount of confidence, forgoing the need for an apolocetic shrug, which I have never ever heard of. Never, and I have a degree in math with a minor in Statistics. Good for you. As you might have guessed from reading that I used to teach statistics, I have a bit more than a minor in the subject. Your attempt to appeal to authority, not to put too fine a point on it, falls flat. Just because you haven’t heard of a thing don’t mean it isn’t true. We can, after all, just read the original paper: > Before I had succeeded in solving my problem analytically, I had endeavoured to do so empirically. The material used was a correlation table containing the height and left middle finger measurements of 3000 criminals, from a paper by W. R. Macdonnell (Biometrika, i, p. 219). The measurements were written out on 3000 pieces of cardboard, which were then very thoroughly shuffled and drawn at random. As each card was drawn its numbers were written down in a book, which thus contains the measurements of 3000 criminals in a random order. Finally, each consecutive set of 4 was taken as a sample—750 in all—and the mean, standard deviation, and correlation5 of each sample determined. The difference between the mean of each sample and the mean of the population was then divided by the standard deviation of the sample, giving us the z of Section III. As for the apologetic shrug, in the course of the “analytic solution” we have: > The law of formation of these moment coefficients appears to be a simple one, but I have not seen my way to a general proof. and then after a bit more math guessing the correct distribution based on the moments > Consequently a curve of Prof. Pearson’s Type III may he expected to fit the distribution of s2. My story is slightly off; Gosset only used one sample size rather than several different sample sizes. But he did use simulation with thousands of hand written cards as his approach to the problem, he did fail to prove the correct distribution (moments are not sufficient to determine the distribution), and he did publish with an apologetic shrug.
jll29 2y ago
Typo: guest of Person => Karl Pearson

0xDEAFBEAD 2y ago

It's interesting how mathematically shallow most stats presentations are. In most other areas I've studied, you start from some basics like axioms and gradually build up machinery by proving theorems etc. But presentations I've seen of the t-test focus on when and how to use it, without going very deep into the derivation at all. This leaves me skeptical of the movement to replace calculus with stats in high school. It's true that an ordinary citizen will find stats more useful. But for students who will go on to become scientists and engineers, I think they should study calculus. Calculus is a better on-ramp to the sort of rigor you need in upper-level math. And I'm concerned that a bad "cargo cult" stats class may be worse than no stats education at all. Calculus education seems harder to screw up.

blt 2y ago
Not sure why you are downvoted for this. Your points have merit. I agree that stats classes can have a "cookbook" flavor and do not generally lead to a deep understanding of probability. But I would rather fix the stats classes than abandon the topic. Does anyone really argue to replace calculus with stats? I thought the idea was to offer both and let students choose based on their interests.
- jll29 2y ago
  Propbabilities, combinatorics, logics and sets are the most valuable things from high school maths that benefitted me all the way through from teenager to professor. Calculus is intellectually stimulating, but for my line of work (dealing with uncertaintly, risk, decision making, AI), other parts of mathematics are more useful. However, I would not argue calculus should be replaced. I would argue for more "proper" maths to replace "recipe-like" maths. It's more important to go deeper on a topic than what the topic is.
  - CrazyStat 2y ago
    Combinatorics would make a great high school math course, honestly. Lots of fun puzzles and very approachable.
  - 2y ago