The importance of being wrong
19 August 2013
Open Letter to Khan Academy about Basic Probability
2 September 2013

Statistics is not really elegant or even fun in the way that a mathematics puzzle can be. But statistics is necessary, and enormously rewarding. I like to think that we use statistical methods and principles to extract truth from data.
This week many of the high school maths teachers in New Zealand were exhorted to take part in a Stanford MOOC about teaching mathematics. I am not a high school maths teacher, but I do try to provide worthwhile materials for them, so I thought I would take a look. It is also an opportunity to look at how people with an annual budget of more than 4 figures produce on-line learning materials. So I enrolled and did the first lesson, which is about people’s attitudes to math(s) and their success or trauma that has led to those attitudes. I’m happy to say that none of this was new to me. I am rather unhappy that it would be new to anyone! Surely all maths teachers know by now that how we deal with students’ small successes and failures in mathematics will create future attitudes leading to further success or failure. If they don’t, they need to take this course. And that makes me happy – that there is such a course, on-line and free for all maths teachers. (As a side note, I loved that Jo, the teacher switched between the American “math” and the British/Australian/NZ “maths”).
I’ve only done the first lesson so far, and intend to do some more, but it seems to be much more about mathematics than statistics, and I am not sure how relevant it will be. And that makes me a bit sad again. (It was an emotional journey!)
Mathematics in its pure form is about thinking. It is problem solving and it can be elegant and so much fun. It is a language that transcends nationality. (Though I have always thought the Greeks get a rough deal as we steal all their letters for the scary stuff.) I was recently asked to present an enrichment lesson to a class of “gifted and talented” students. I found it very easy to think of something mathematical to do – we are going to work around our Rogo puzzle, which has some fantastic mathematical learning opportunities, but sadly is no more! (added March 2018) But thinking up something short and engaging and realistic in the statistics realm is much harder. You can’t do real statistics quickly.
On my run this morning I thought a whole lot more about this mathematics/statistics divide. I have written about it before, but more in defense of statistics, and warning the mathematics teachers to stay away or get with the programme. Understanding commonalities and differences can help us teach better. Mathematics is pure and elegant, and borders on art. It is the purest science. There is little beautiful about statistics. Even the graphs are ugly, with their scattered data and annoying outliers messing it all up. The only way we get symmetry is by assuming away all the badly behaved bits. Probability can be a bit more elegant, but with that we are creeping into the mathematical camp.

English Language and English literature

I like to liken. I’m going to liken maths and stats to English language and English literature. I was good at English at school, and loved the spelling and grammar aspects especially. I have in my library a very large book about the English language, (The Cambridge encyclopedia of the English Language, by David Crystal) and one day I hope to read it all. It talks about sounds and letters, words, grammar, syntax, origins, meanings. Even to dip into, it is fascinating. On the other hand I have recently finished reading “The End of Your Life Book Club” by Will Schwalbe, which is a biography of his amazing mother, set around the last two years of her life as she struggles with cancer. Will and his mother are avid readers, and use her time in treatment to talk about books. This book has been an epiphany for me. I had forgotten how books can change your way of thinking, and how important fiction is. At school I struggled with the literature side of English, as I wanted to know what the author meant, and could not see how it was right to take my own meaning from a book, poem or work of literature.  I have since discovered post-modernism and am happy drawing my own meaning.
So what does this all have to do with maths and statistics? Well I liken maths to English language. In order to be good at English you need to be able to read and write in a functional way. You need to know the mechanisms. You need to be able to DO, not just observe. In mathematics, you need to be able to approach a problem in a mathematical way.  Conversely, to be proficient in literature, you do not need to be able to produce literature. You need to be able to read literature with a critical mind, and appreciate the ideas, the words, the structure. You do need to be able to write enough to express your critique, but that is a different matter from writing a novel.  This, to me is like being statistically literate – you can read a statistical report, and ask the right questions. You can make sense of it, and not be at the mercy of poorly executed or mendacious research. You can even write a summary or a critique of a statistical analysis. But you do not need to be able to perform the actual analysis yourself, nor do you need to know the exact mathematical theory underlying it.

Statistical Literacy?

Maybe there is a problem with the term “statistical literacy”. The traditional meaning of literacy includes being able to read and write – to consume and to produce – to take meaning and to create meaning. I’m not convinced that what is called statistical literacy is the same.
Where I’m heading with this, is that statistics is a way to win back the mathematically disenfranchised. If I were teaching statistics to a high school class I would spend some time talking about what statistics involves and how it overlaps with, but is not mathematics. I would explain that even people who have had difficulty in the past with mathematics, can do well at statistics.
The following table outlines the different emphasis of the two disciplines.

Proficiency with numbers is importantProficiency with numbers is helpful
Abstract ideas are importantConcrete applications are important
Context is to be removed so that we can model the underlying ideasContext is crucial to all statistical analysis
You don’t need to write very much.Written expression in English is important

Another idea related to this is that of “magic formulas” or the cookbook approach. I don’t have a problem with cookbooks and knitting patterns. They help me to make things I could not otherwise. However, the more I use recipes and patterns, the more I understand the principles on which they are based. But this is a thought for another day.


  1. John Bibby says:

    I think the key difference comes about because statistics is the “science of evidence” – it is not about numbers; and mathematics is not evidence – it is logic.
    They have different dynamics. But both can be beautiful!

  2. drgood says:

    Suggest you read “Brazzaville Beach” as it contrasts the two types of mathematicians.

  3. janacek says:

    You can only say that “there is little beautiful about statistics” if you have never looked at design of experiments or generalised linear models. The advantage of statistics is that it is even more exciting to actually deal with the data and understand what lies behind it.
    I would argue Statistics in its pure form is about thinking. It is problem solving and it can be elegant and so much fun!

  4. Glenn Fulford says:

    A couple of comments on this interesting blog post.
    1. On the stanford MOOC course. You were disappointed because you thought the course was teaching nothing that an experienced teacher didn’t already know. However, I think that such a course is probably more for people who are interested in getting into teaching rather than experienced teachers. It think it could be a good way to sample whether they might be interested in doing an education degree or not without the expense of starting a degree.
    2. I have a mathematical modelling background. It seems to more in common with Statistics than “pure” mathematics, yet statistics still seems very different to me than mathematical modelling. Perhaps it fits somewhere between the two?

  5. Jamie Sneddon says:

    It’s interesting that you say that “You can’t do real statistics quickly.” I completely agree. Real statistics goes through the PPDAC cycle at least once – it’s messy and complicated and interesting. It is possible to do some ‘statistics’ quickly. You could be told the problem to be investigated, and how to investigate it (and sometimes even be given the data). You can do the procedural parts of statistics quickly.
    I would argue that mathematics is the same. You can’t do real mathematics quickly. Sure, you can find the derivative of f(x) = x + 1/x, and maybe also find the stationary points, but that’s only one small part of a mathematical problem. Authentic mathematical problems start with open-ended (possibly real-world) questions and build the mathematics on the go; questions like “I wonder if it’s possible to jump from one car of a Ferris wheel to the car below?” And the best answers to mathematical problems lead to new questions and investigations in much the same that a statistical conclusion often raises a new problem (the link from C back to P).

  6. I think the points in the table for mathematics and statistics can be applied to both. In certain fields of mathematics which involve mathematical modeling, context and assumptions are important in the models. Proficiency with numbers is helpful and important for both mathematics and statistics.
    The statement “Statistics is not really elegant or even fun in the way that a mathematics puzzle can be. ” is subjective but everyone is entitled to an opinion. I used to like theoretical math/stats and some proofs but have shifted to applied statistics with some statistical computing.

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