> 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.”
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.
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).
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.
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.
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.
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.
100% agree. Both calculus and probability can be used successfully as a vehicle to teach rigorous though, which is the real point of math education.
Rate of change, slopes, finding maximal points etc is extremely important in all of that, and that concept you learned and got intuition for in calculus. Calculus isn't worthless for you at all, you just undervalue it.
You might not have needed to study more calculus than the original courses, but that just makes that course even more valuable, it is so useful in so many domains even though it is a low level math class.
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.
You can see the derivatives based on their shapes, it is very intuitive that way unlike statistics. Calculus tries to show the intuitive explanations for the different parts, and it works very well it is how we get engineers and those engineers has built almost everything we see in modern society.
Intuition is much more useful than formalism unless you need to prove things, and calculus is one of the most intuitive subjects in math once it clicks. That intuition then stays with students for their entire lives, often they don't understand they got it from calculus class. Humans has very poor intuition for things like velocity and acceleration until after they take calculus, but people forget that since those things feels so extremely obvious after you have taken the class. That just shows how great the class is, that it helps solidify such important concepts that people don't even realize they used to have trouble with them.
> Unfortunately intro stats classes often fail on this count as well
Because unlike calculus statistics is very unintuitive. The only ways to teach it is either via extreme formalism or by showing people what numbers to put where, there is no intuitive way to teach statistics as far as we know. That makes statistics classes and knowledge you learn there churn much faster than the intuition built in calculus, making the class inherently less useful.
All the useful things I know about statistics I learned in middle school, stuff like confidence intervals, sampling bias etc. Everyone learns that in middle school, later stats classes just focus on churning numbers, I learned nothing in later stats classes I was forced to take in college.
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...
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
I see what you did there
Abelson, R. P. (1995). Statistics as Principled Argument. Psychology Press. https://www.routledge.com/Statistics-As-Principled-Argument/...
> In this illuminating volume, Robert P. Abelson delves into the too-often dismissed problems of interpreting quantitative data and then presenting them in the context of a coherent story about one's research. Unlike too many books on statistics, this is a remarkably engaging read, filled with fascinating real-life (and real-research) examples rather than with recipes for analysis. It will be of true interest and lasting value to beginning graduate students and seasoned researchers alike. The focus of the book is that the purpose of statistics is to organize a useful argument from quantitative evidence, using a form of principled rhetoric. Five criteria, described by the acronym MAGIC (magnitude, articulation, generality, interestingness, and credibility) are proposed as crucial features of a persuasive, principled argument. Particular statistical methods are discussed, with minimum use of formulas and heavy data sets. The ideas throughout the book revolve around elementary probability theory, t tests, and simple issues of research design. It is therefore assumed that the reader has already had some access to elementary statistics. Many examples are included to explain the connection of statistics to substantive claims about real phenomena.
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_...
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).
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 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 personally found a lot of peace after learning that tidbit.