Great scientist - statistics = lots of failed experiments

E.O. Wilson is a famous evolutionary biologist. He is currently an emeritus professor at Harvard and just this last week dropped this little gem in the Wall Street Journal. In the piece, he suggests that knowing mathematics is not important for becoming a great scientist. Wilson goes even further, suggesting that you can be mathematically semi-literate and still be an amazing scientist. There are two key quotes in the piece that I think deserve special attention:

Fortunately, exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory. Far more important throughout the rest of science is the ability to form concepts, during which the researcher conjures images and processes by intuition.

I agree with this quote in general as does Paul Krugman. Many scientific areas don't require advanced measure theory, differential geometry, or number theory to make big advances. It seems like this is is the kind of mathematics to which E.O. Wilson is referring to and on that point I think there is probably universal agreement that you can have a hugely successful scientific career without knowing about measurable spaces.

Wilson doesn't stop there, however. He goes on to paint a much broader picture about how one can pursue science without the aid of even basic mathematics or statistics and this is where I think he goes off the rails a bit:

Ideas in science emerge most readily when some part of the world is studied for its own sake. They follow from thorough, well-organized knowledge of all that is known or can be imagined of real entities and processes within that fragment of existence. When something new is encountered, the follow-up steps usually require mathematical and statistical methods to move the analysis forward. If that step proves too technically difficult for the person who made the discovery, a mathematician or statistician can be added as a collaborator.

I see two huge problems with this statement:

  1. Poor design of experiments is one of, if not the most, common reason for an experiment to fail. It is so important that Fisher said, "To consult the statistician after an experiment is finished is often merely to ask him to conduct a post mortem examination.  He can perhaps say what the experiment died of." Wilson is suggesting that with careful conceptual thought and some hard work you can do good science, but without a fundamental understanding of basic math, statistics, and study design even the best conceived experiments are likely to fail.
  2. While armchair science was likely the norm when Wilson was in his prime, huge advances have been made in both science and technology. Scientifically, it is difficult to synthesize and understand everything that has been done without some basic understanding of the statistical quality of previous experiments. Similarly, as data collection has evolved statistics and computation are playing a more and more central role. As Rafa has pointed out, people in positions of power who don't understand statistics are a big problem for science.

More importantly, as we live in an increasingly data rich environment both in the sciences and in the broader community - basic statistical and numerical literacy are becoming more and more important. While I agree with Wilson that we should try not to discourage people who have a difficult first encounter with math from pursuing careers in science, I think it is both disingenuous and potentially disastrous to downplay the importance of quantitative skill at the exact moment in history that those skills are most desperately needed.

As a counter proposal to Wilson's idea that we should encourage people to disregard quantitative sciences I propose that we build a better infrastructure for ensuring all people interested in the sciences are able to improve their quantitative skills and literacy. Here at Simply Stats we are all about putting our money where our mouth is and we have already started by creating free, online versions of our quantitative courses. Maybe Wilson should take one....

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  • http://twitter.com/hspter Hilary Parker

    The armchair science thing is a good point. I saw another great reaction to his piece, which brought up the fact that E.O. Wilson had this crazy "gay uncle" theory which was 1) not supported by data, and 2) not even theoretically correct due to shoddy math. http://westhunt.wordpress.com/2013/04/09/math-is-hard/ Armchair science not-FTW.

    However if this results in E.O. Wilson barbie dolls that say "Math is hard!" then maybe it was all worth it.

  • Walter Reade

    I have an uncle who has done extensive research in molecular pathology at MD Anderson. Last summer I asked him about his statistics/data analysis methods. I was surprised when he said he didn't so much. He said the challenging part of the job was understanding the biology and coming up with novel ideas. The experiments were generally straight forward and gave clear indications whether the hypothesis was correct or not.

    • Ken

      If you understand one simple design, and stick to it, then it will work OK. The problem is that a lot of researchers don't understand important concepts like blocking. It doesn't stop them analysing the data, just gives incorrect results.

  • Walter Reade

    Oh, and I'll flat out state that I don't like Krugman's remarks that "mathematical intuition is crucial" (more-so than actually knowing the math). I don't think the authors (or readers) of this blog need too much convincing that human intuition is TERRIBLE and leads to all sorts of problems in the sciences.

    • dkural

      I am a mathematician and agree with the blog post. I am with you that humans have a whole slew of built-in systematic errors (along the lines of Daniel Kahneman). I do think a separate thing called intuition does exist though. Here's something to think about: Before the proof, there is intuition. How would anyone prove a theorem for the first time, from scratch? If ones intuition is terrible; it simply means one doesn't have good intuition. A hunch / inclination is a different thing from intuition. Likewise; this doesn't mean one follows their intuition without further checks of logic + conscious analysis.

  • ezracolbert

    you do realize, that for those of us who do Wilsonian science, all you are doing is demonstrating, to a high degree of confidence, that you don't know what it is we do ?

    I know this might be kind of a shocker, you might want to sit down first, but , instead of spouting off on your blog, how about chatting with a few colleagues first ?
    Maybe someone in biology or chemistry....

    I hope you also realize that Great Statisticians, without guides to the real world = great statistics but terrible science ? LIke the guy who was on Gelman's blog recently, claiming to have something interesting from data dredging p values from abstracts ?

    every time I have actually talked to a professional statistician, it has been a total waste of time; no matter how much I simplified what it was taht i was trying to say, they couldn't understand me - and I've had a lot of objective feedback that I can explain things well to non specialists; as one engineer told me, you are the only PhD I've ever met who actually trys to explain stuff to engineers...

    • http://twitter.com/hspter Hilary Parker

      I think the fascinating thing is that you continue this "total waste of time" of talking to professional statisticians by commenting on this blog. You're clearly so much smarter, and you obviously do not feel any need to prove it!

    • anon

      you are the smartest non-quantitative scientist, who is the only one capable of explaining to non-specialists. yet, because all "professional" statisticians that you talked to do not understand your projects, they have no understanding of science research.

      in this case, the best way to advance your science sounds like learning some statistics on your own (perhaps instead of reading statistics blogs).

      your comment is a perfect example of WHY experimentalists need to talk to statisticians before wasting money on experiments. read Fisher's quote in the post.

      PS: jeff's publication list shows very clearly that he does communicate with experimentalists, successfully.

  • http://twitter.com/Malarky67 Stephen Henderson

    Both EO Wilson and Paul Krugman are probably (kinda) correct though for their fields. Both evolutionary/socio biology and economics are sciences where natural experiments are (generally) not possible. Hence academic reputations have often been attained by chasing down theoretical rabbit-holes. Often these are mathematical (game theory, efficient markets) without really being empirical or testable (except in the "look we blew up the world economy" sense).

    However I know there is a trend in sociobiology not away from mathematics but towards data - and I believe this is the new buzz in economics too e.g.
    http://blogs.wsj.com/economics/2013/04/10/handicapping-the-john-bates-clark-medal-2/

  • Steven Salzberg

    E. O. Wilson has a stellar reputation in biology, but he seems to be deeply confused about mathematical thinking. There's a good takedown of Wilson's comments over at Slate:
    http://www.slate.com/articles/health_and_science/science/2013/04/e_o_wilson_is_wrong_about_math_and_science.html

    by a mathematician from Berkeley. That article also points out that even Wilson's biology has been flawed in recent years, in part because he is pushing models of evolution that require some math - which Wilson doesn't understand. See the critique by Richard Dawkins:
    http://www.prospectmagazine.co.uk/magazine/edward-wilson-social-conquest-earth-evolutionary-errors-origin-species/

    in which he explains that Wilson's new book has "many pages of erroneous and downright perverse misunderstandings of evolutionary theory."

    Wilson made great strides in understanding the social behavior of insects, but unfortunately he has lost all credibility in recent years. I think he's losing it.

  • t.g.

    I think that you sort of missed the spirit of the article.
    As far as I understood it, it was a pledge against excessive reliance on maths:

    "This imbalance is especially the case in biology, where factors in a real-life phenomenon are often misunderstood or never noticed in the first place. The annals of theoretical biology are clogged with mathematical models that either can be safely ignored or, when tested, fail. Possibly no more than 10% have any lasting value. "

    I think that this statement holds true for many areas where maths and statistics are used currently (I can guarantee economics for ex. is full of intellectually sterile, but highly mathematical work).
    For most scientists maths and statistics are just (important) tools- the ideas have to come from some place else.
    More so, the man himself encourages people to work on their maths: "If your level of mathematical competence is low, plan to raise it".

  • jake

    There are good reasons why scientist choose to study certain things and statisticians need to respect that.

    Perhaps, the best example of how stupid statisticians can make themselves appear is from the father of the field Fisher.

    From the wikipedia page:-

    "Fisher was opposed to the conclusions of Richard Doll and Austin B. Hill that smoking causes lung cancer. He compared the correlations in their papers to a correlation between the import of apples and the rise of divorce in order to show that correlation does not imply causation.[29]"

    To give good advice it helps if the statisticians learn some science (and don't enjoy smoking/ being paid by the tobacco industry!)