Interesting read. I don't think this came up in my stats classes:
Gosset solved many problems at the brewery with his new technique. The self-taught statistician published his t-test under the pseudonym “Student” because Guinness didn’t want to tip off competitors to its research. Although Gosset pioneered industrial quality control and contributed loads of other ideas to quantitative research, most textbooks still call his great achievement the “Student’s t-test.”
I always thought that name was strange but I never thought to look it up. Stats books are so dry, they don’t have the inclination to share these kinds of stories.
You probably missed it. This is something stat book authors love to mention. I don’t remember a stat intro book that doesn’t have a footnote for “Student t”.
Just went through mine a few months ago. It definitely doesn't have it.
what book? i'm honestly curious because of how frequently this story is repeated in stats textbooks
The author is Jay Devore.
Doubly unfortunate because the philosophical aspects of statistics are more important to students than most of maths. There are something like 4 different schools of thought [0] and people will have a natural propensity to one of them.
Although they all agree on the formulas and rigorous aspects, it is actually a challenging proposition to comprehend what someone is doing if you strongly see the world from one perspective and don't realise that academics are potentially approaching the interpretation in one of 3 other ways.
It adds a lot of dryness to the textbook because the author can really only talk about the objective parts in an introductory classroom setting. But if you're getting taught by a frequentist and have a subjectivity bent it is easy to spend a year or two confused before someone clues you in that there are unresolved questions of interpretation.
[0] https://en.wikipedia.org/wiki/Interpretation_of_probability
Interesting, my university book of the subject was pretty tiny but it did talk of the different interpretations, but it only mentioned frequentist and bayesian. I did not suspect the story was much more complicated.
I see what you did there
It doesn't have to be that way. My pandemic lockdown read was a 10 dollar Stats textbook[1], that comes with tons of classic examples: the Salk polio vaccine, a prosecutor misusing the multiplication rule using purely circumstantial evidence ("what are the odds that police pulled over the wrong couple matching 10 different pieces of description by the victim?"), the classic Gallup poll showing FDR would defeat Landon (versus incumbent _Literary Digest_ showing a Landon win), Gosset's history with Guiness, the early history of probability as gambling strategy, a controversy over Mendel's data on pea plant heredity being _too_ clean, and so on.
Sadly, while this book left me well prepared to apply statistical reasoning in my day job, it's departure from typical pedagogy left me feeling unprepared for further reading based on perusal of Stats Wikipedia -- what's a kernel? what's a moment? etc.
[1]: https://www.amazon.com/Statistics-Fourth-David-Freedman-eboo...
In a former life I taught some intro stat courses from this book. It’s a good book for an intro course for people who aren’t going on to further stat classes, although I think for a current class I’d want something that acknowledges how statistics and computers have gotten all tied up with each other. (I don’t have any recommendations - it’s not my job to know this any more.)
The history of just about anything is very interesting, but it's generally not relevant in a textbook which has a specific purpose.
I agree with the sentiment, but I always have wondered what t-test a real engineer uses and why they only teach the "Student" version. Given the context, a bit of a clarifier would have been appreciated.
sorry but this is a classic story mentioned in almost every basic stats textbook i’ve read
I liked this one a lot
Abelson, R. P. (1995). Statistics as Principled Argument. Psychology Press. https://www.routledge.com/Statistics-As-Principled-Argument/...
Wait until you hear about the bad blood between Fisher and Pearson.
I wonder if dry reading means written without the influence of drink. I couldn't find an answer online. But, if so, it would be ironic to describe a stat book that ignored a brewer as dry.
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.
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.
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.
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.
Combinatorics would make a great high school math course, honestly. Lots of fun puzzles and very approachable.
Calculus is also mathematically shallow in that sense: the subject where you start with axioms and gradually build up the machinery of calculus is (Real) Analysis, which is not part of the standard calculus curriculum and which the vast majority of people taking calculus will never study [1]. A typical Calculus class expects students to memorize and use things like trig function integrals which are presented without proof; not so different from memorizing and using statistical tests presented without proof, in my opinion.
In an intro statistics class I think conceptual depth is more important than mathematical depth. It's more important that students really understand the concept of probabilistic inference, both hypothesis tests and confidence intervals, than that they understand the mathematical derivation of the t distribution [2].
Unfortunately intro stats classes often fail on this count as well. One of the (many) straws that eventually broke my desire to teach was a committee decision--a committee composed entirely of people not teaching intro stats--to disallow students from bringing formula cheatsheets to exams, effectively forcing us to make the students memorize formulas rather than focusing on conceptual understanding.
[1] When I took Real Analysis there was a calculus class that met right before us in the same room, which often ran over so that the calculus students would be packing up as we entered the room. One day as we're sitting down one of them asks us what class we're there for, and then asks what Real Analysis is all about, since he's never heard of it. One of my classmates responded with the absolutely perfect "Well, our homework last night was integrating x^2 from 0 to 1."
[2] I'd say the same goes for Calculus, for what it's worth; actually understanding what an integral means is more important than being able to set up the Reimann sum and take the limit.
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.
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).
Typo: guest of Person => Karl Pearson
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:
As for the apologetic shrug, in the course of the “analytic solution” we have:
and then after a bit more math guessing the correct distribution based on the moments
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.
along with compulsory Guinness tasting :)
At least they let him publish, albeit under a pseudonym. It makes me wonder how many potentially useful discoveries were made in industrial settings, and wound up being buried due to management not wanting to risk leaking competitive information. The good news, I suppose, would be if you believe that it's rarely the case that only one person could ever discover something. Then you can conclude that all (most?) such discoveries were eventually (or will eventually be) rediscovered independently.
On a related note... I wonder how much valuable research disappears (more or less) when companies fold, get acquired, etc. Take MCC[1] for example. I've been doing a lot of reading lately that involves old papers from the 1990's on "agents" and "multi-agent systems". And time and time again, in the references, you'll see something like "MCC Technical Report TR86-32791" or some-such. Occasionally said report can be found online, but quite a few of them seem to be either hard - or impossible - to find. Maybe there's an archive of physical papers stored away somewhere, but FSM knows where the heck such a thing would be, or how hard it would be to get access.
A similar situation came up a while back when we started discussing "sharding" here on HN[2]. There was a lot of effort spent trying to identify when the term first arose, and a lot of evidence pointed to a particular paper that was internal to CCA, who were acquired by Xerox. And now that original paper seems to be unobtanium. The paper probably still exists somewhere in the bowels of Xerox, but good luck ever getting your hands on it.
[1]: https://en.wikipedia.org/wiki/Microelectronics_and_Computer_...
[2]: https://news.ycombinator.com/item?id=36848605
Probably a lot. I’ve come to find out that some dinosaur companies won’t even let their programmers open up issues on open source repos (forget sending patches or releasing their own software).
The logic goes like this: if someone found the log4j zero day before it was reported they could comb through all issues and see the companies that the users worked for then try to target them. In this case any comment would indicate possible involvement.
The least bit of security, through the tiniest extra bit of obscurity. Thankfully many of these companies are starting to come around and realizing that a lack of involvement with open source is more risky than accidental 3rd hand information leaking (like what dependencies doesn’t certain company use).
The easiest counter to this is that, to my knowledge at least, it’s easier to build a vulnerability scanner than to scrape repos for more targeted attacks.
The "No lieutenant, your men are already dead" defense. I like it.
I think that if your threat model includes nation states (and the companies I was referencing above was largely S&P500 financial institutions) then you have to think the attacker also doesn’t want to trip off any alarms with a ham fisted port scan blasting the precious zeroday exploit all over the internet. Your point is still extremely valid though.
Which is why the counter I provided is that the best defense is to get as many engineers’ eyes on the problem and in the codebase as possible to prevent or find it before it becomes an issue. Things like lib XZ are scary, but it’s even scarier if not caught before it’s in the wild.
The dirty secret is that nation states can get your software dependency list pretty easily in a number of ways (e.g. sending agents to meetups to nerd out & make friends would be an expensive way but there’s other social engineering attacks I’ve observed).
The other secret is that monitoring software can’t detect anomalies ahead of time & the vulnerability scan will not show up meaningfully any different than all the other random traffic already happening. Your nation state can hide it’s vulnerability scan amongst all the other vulnerability scanners already running (both legit as a service when you request it against your server & illegitimate actors trying to find a way in). So at best a ham fisted search is unlikely to really tip your hand in a meaningful way unless it requires having penetrated a few layers of your security to begin with.
As for libxz, the scary part is that as an industry we recognize the security challenge of not compensating maintainers and yet we have lackluster responses to fixing it (e.g. Google trying to pay OSS maintainers to harden their security while completely ignoring that a huge problem is that the maintainers can’t devote full time which opens an avenue for malicious actors to overwhelm maintainers & take control socially as happened with libxz).
I always found "student" confusing in the name. Like, is there a "professors t-test" or something?
I personally found a lot of peace after learning that tidbit.
This was in my textbook and my professor covered it as well! Class of 17 here
54 years after I was mystified trying to parse the use of "student" for this, here is the answer. Cool!
Many international conferences are regularly held in Dublin, and attendees often visit the Guinness brewery as part of conferences' social events, where a memorial plaque reminds them of Gosset and his important contributions to statistics.