Meta: When I clicked the link from HN (or from the WSJ front page), I got 2 paragraphs and a paywall. But using Google on a line of the text sets it up so you get the article.
Statistics is a very interesting subject, and it is a distinct subject from mathematics proper. Here (in what is becoming a FAQ post for HN) are two favorite recommendations for free Web-based resources on what statistics is as a discipline, both of which recommend good textbooks for follow-up study:
"Advice to Mathematics Teachers on Evaluating Introductory Statistics Textbooks" by Robert W. Hayden
I have encountered some recent examples of people finding interesting work by being able to step into the intersection of computer science and statistics, with a strong pure math background besides. A lot of statistical researchers need programming help, and a lot of programmers need to be more aware of statistical issues. It's a win-win when a learner learns a lot about math, statistics, and computer science.
I like your comment. Let me add a second view-point to your first sentence.
> Statistics is a very interesting subject, and it is a distinct subject from mathematics proper.
Mathematics proper is more than one subject, already. (Theoretical) computer science and statistics are just two more branches of math.
The notion of statistics as being outside math remains me a bit of how thermodynamics was viewed as not proper physics (or prober chemistry) in the 19th century.
The study of thermodynamics got a huge boost from the commercial need to understand and build better steam engines. If you look close enough, thermodynamics is actually statistics. (And of course statistics and probability theory is just applied measure and integration theory.)
reminds me of a comment a classmate used to make (we were taking a course together on measure theory, taught in the statistics dept. which was separate from our math dept.); "Inside every hard statistics problem is a trivial analysis problem struggling to get out"
Our teaching assistent for probability theory gave us real hard nuts to crack. And he was strict about the rigour of our answer--we often had to ground our proofs in measure theory to get past his radar. And he allowed no handwaiving.
The demands were a bit annoying at the time, but I credit him with getting a understanding of probability theory. I wish every course would have been like this.
I kind of agree that statistics should be viewed as slightly different subject from math proper. The math aspect of statistics is not, in itself, the important aspect. The interesting (and in my opinion harder) aspect is the more subjective part of getting a good feel for how to pick from the myriad of statistical tests available to use on your data and to analyse exactly what the results from those tests mean relative to your data.
Both of those aspects are core to applying statistics and neither are purely mathematical. Both are also often ignored or marginalized by those who simply see statistics as applied analysis-light.
Actually, picking tests is a purely mathematical topic. The only reason it feels like an art and not math is because people still use frequentist statistics.
Picking an optimality criterion for your tests is an art. Then picking optimal tests is pure math. But for anything beyond toy problems picking an optimal test (or optimal parameters for your test), so there comes the black art part in again.
What do you pronounce as the alternative to frequentist statistics? May I guess you'd pick Bayesian approaches?
Mathematical things like maximum likelihood estimators can be seen as solving a min-max problem atop of Bayesian calculations.
Thanks for your reply. What I refer to in my grandparent post is the core issue that statistics is about DATA--it is very different from any branch of pure mathematics in that regard, as the first link in my previous post makes clear.
I would be fascinated to hear comparisons of the performance of graduates of different disciplines as developers. I know we everyone can think of a few examples of good and bad for all; but it would be interesting to collate large numbers of peer reviews and see if any disciplines stand out.
In the eight companies I have worked for, I think it's quite likely the maths graduates stand out. If not maths then probably electrical engineering. The chemistry and physics graduates are widely distributed. I know a lot of computer science graduates but I would hesitate to categorise any as great developers. A hundred or so is a terribly small sample so I would love to see results from a decent sample.
(It happens I am about to start recruiting again, and no, I'm not a maths graduate.)
I never did manage to get a job with my chemistry degree, and now I am decades out of date. With the small amount of programming I do these days I'm probably out of date with that now too. :-( I have only worked with two chemistry majors that I know of - and they were wildly different to each other.
I am a fan of peer reviews as opposed to what managers think is going on - so I would personally not discard people's opinions about who the best developers in their group were.
I can easily think of a list of developers at the places I've worked who would have been regarded as outstanding - and I believe every developer working at those places would have about the same list.
Why? The difference in skill between programmers is huge, but only a tiny amount of that variance could be predicted by the programmer's major. This is as misguided as discarding everyone who doesn't have a 4.0 GPA or didn't go to a top-10 school.
I suspect the average math undergrad is not as good a programmer as the average CS undergrad (but my sample is restricted to my college).
However, if we count only the maths majors who end up working as programmers then I believe there will be some significant self-selection. So if such a study were done I wouldn't be surprised if math and physics majors were found to be better than CS majors.
In any case I'd agree with you that in that I would never blindly use that in a hiring process.
My experience has been that there really isn't a strong correlation between what degree you hold and your ability as a developer. But I've only worked with about 20, so my sample set is significantly smaller than yours.
The best was an incomplete theory-heavy B.A. in CS from UofIowa, with a close runner-up being an EE from a university in India with a name I've since forgotten. I'm guessing it was their best engineering school because this guy was wicked smart and left to do grad work at CMU, and now works for (I think) Google in London.
Worst: Degree-milled Ph.D in Astrophysics. Runner-up: CS degree from UIUC (circa 1993).
BTW, don't be terribly surprised by CS majors not leading the pack in software development. Even with a coding-heavy curriculum, you're looking at a student who has to write maybe 100,000 LOC over a 4 year duration, in an environment where expectations are exceedingly low for SD skills. In academia, there really aren't any coding role-models to set them straight on proper techniques, design patterns, style, SCM, debugging, documentation, etc -- that is, unless, they read, filter, practice/experiment, and internalize some of the gems that float around on proggit/HN/etc.
Mathematicians probably do quite well, because thanks to the Curry-Howard Isomorphism (http://en.wikipedia.org/wiki/Curry–Howard_correspondence) they are forced to write a lot of small programs that are intensely scrutinized for any bugs or gaps. And they are also forced to read lots of very good programs and be able to explain them.
In my linear algebra, number theory and optimization classes the correspondence between the proofs and (functional) programs was especially easy to see.
>>>>Employees teach new recruits to use tools for comparing the performance of one version of a feature with another and how to determine what sort of difference in response is meaningful.>>>>>
I hate when people use statistical significance to determine what is meaningful. People wrongfully think you need 95% confidence in the data to make a decision and move forward with a feature change, etc. For me when I am changing things on my site based on data mining, I will make a decision with a 60% confidence (which can come within 5-10 samples in most cases). Hacking websites is engineering not science! Overall it makes sense to trade a low confidence value for speed of development.
Statistical significance is also not even a sufficient condition for a difference to be meaningful. In the real world, very few things are truly identical, so you can eventually get a statistically significant difference for just about any comparison, given enough samples. But the differences may be negligibly small.
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"Advice to Mathematics Teachers on Evaluating Introductory Statistics Textbooks" by Robert W. Hayden
http://statland.org/MyPapers/MAAFIXED.PDF
"The Introductory Statistics Course: A Ptolemaic Curriculum?" by George W. Cobb
http://repositories.cdlib.org/cgi/viewcontent.cgi?article=10...
Both are excellent introductions to what statistics is as a discipline and how it is related to, but distinct from, mathematics.
A very good list of statistics textbooks appears here:
http://web.mac.com/mrmathman/MrMathMan/New_Teacher_Resources...
I have encountered some recent examples of people finding interesting work by being able to step into the intersection of computer science and statistics, with a strong pure math background besides. A lot of statistical researchers need programming help, and a lot of programmers need to be more aware of statistical issues. It's a win-win when a learner learns a lot about math, statistics, and computer science.
> Statistics is a very interesting subject, and it is a distinct subject from mathematics proper.
Mathematics proper is more than one subject, already. (Theoretical) computer science and statistics are just two more branches of math.
The notion of statistics as being outside math remains me a bit of how thermodynamics was viewed as not proper physics (or prober chemistry) in the 19th century.
The study of thermodynamics got a huge boost from the commercial need to understand and build better steam engines. If you look close enough, thermodynamics is actually statistics. (And of course statistics and probability theory is just applied measure and integration theory.)
The demands were a bit annoying at the time, but I credit him with getting a understanding of probability theory. I wish every course would have been like this.
Both of those aspects are core to applying statistics and neither are purely mathematical. Both are also often ignored or marginalized by those who simply see statistics as applied analysis-light.
What do you pronounce as the alternative to frequentist statistics? May I guess you'd pick Bayesian approaches?
Mathematical things like maximum likelihood estimators can be seen as solving a min-max problem atop of Bayesian calculations.
Out of curiosity, are you an EE?
However, if we count only the maths majors who end up working as programmers then I believe there will be some significant self-selection. So if such a study were done I wouldn't be surprised if math and physics majors were found to be better than CS majors.
In any case I'd agree with you that in that I would never blindly use that in a hiring process.
The best was an incomplete theory-heavy B.A. in CS from UofIowa, with a close runner-up being an EE from a university in India with a name I've since forgotten. I'm guessing it was their best engineering school because this guy was wicked smart and left to do grad work at CMU, and now works for (I think) Google in London.
Worst: Degree-milled Ph.D in Astrophysics. Runner-up: CS degree from UIUC (circa 1993).
BTW, don't be terribly surprised by CS majors not leading the pack in software development. Even with a coding-heavy curriculum, you're looking at a student who has to write maybe 100,000 LOC over a 4 year duration, in an environment where expectations are exceedingly low for SD skills. In academia, there really aren't any coding role-models to set them straight on proper techniques, design patterns, style, SCM, debugging, documentation, etc -- that is, unless, they read, filter, practice/experiment, and internalize some of the gems that float around on proggit/HN/etc.
In my linear algebra, number theory and optimization classes the correspondence between the proofs and (functional) programs was especially easy to see.
I hate when people use statistical significance to determine what is meaningful. People wrongfully think you need 95% confidence in the data to make a decision and move forward with a feature change, etc. For me when I am changing things on my site based on data mining, I will make a decision with a 60% confidence (which can come within 5-10 samples in most cases). Hacking websites is engineering not science! Overall it makes sense to trade a low confidence value for speed of development.