Education, Education, Education

There is a radio programme called The Museum of Curiosity, in which guests are asked to donate items to this virtual museum, and to explain why they have a particular interest in their donations. There are no rules as to what can and cannot be donated. Donations in the past have included Epping Forest (I might have a story about that for you in a future blog), the yeti and the Asian giant hornet. A year or so ago, I was wondering what I might donate, and I decided it would be a book: Letters from WS Gosset to RA Fisher.

When I started this blog, I resolved never to talk shop. This is where I cave in. I am reminded of Spike Milligan’s opening epigram to Adolph Hitler: My Part in his Downfall. Spike’s preface was, ‘After Puckoon, I swore I would never write another novel: this is it.’

Gosset and Fisher were giants of the science of statistics in the early 20^th century. Sir Ronald Fisher is credited with being the father of statistical methods, although there is a case for Karl Pearson holding this honour. Anyway, the interesting point in terms of a donation to the museum is something in one of Gosset’s letters to Fisher. I should say here that in my lectures, I often note that statisticians use the word interesting in a very specialist sense. When a statistician says that something is interesting, it usually means that it is difficult to think of anything less interesting. However, bear with me, and for the moment, please put up with the reason for Gosset’s fame as a statistician.

In an experiment, it is not enough to know the size of an estimated effect, for example the difference in average cholesterol levels between two groups of people receiving two separate cholesterol-lowering drugs. To assess whether the difference is real, one also needs to know the uncertainty, or variability, of the estimate. Now, one can obtain an estimate of that variability from the same experiment. However, that estimate of the variability is not a fixed quantity, but itself is subject to uncertainty. In principle, one could estimate the margin of uncertainty round the estimated uncertainty of the effect. But that in turn would be subject to uncertainty too… And so the long day wears on.

Gosset cut through all that by working out the distribution of an estimated effect divided by its estimated uncertainty, so that we no longer needed to know the uncertainty exactly. This was the t-distribution, and since then, what is known as Student’s t-test has become ubiquitous, pervading pretty much all branches of science. Gosset published under the pseudonym Student, as at the time he was working for Arthur Guinness, Son and Company, producer of the famous Guinness Stout, and a high-handed employer who would have fired him for moonlighting had they known he was also publishing his statistical researches.

But that is not the interesting thing. When I was a final year maths student, I spent a lot of time swotting in the library, but I used to take time off from studying for my exams by idling around the bookshelves, flipping through volumes selected at random. One day, in the maths library, I was dipping into Letters from WS Gosset to RA Fisher when I came across one missive noting that Fisher, an enthusiast of home-brewed beer, was having little success with brewing stout. I cannot remember the exact wording, but Gosset’s letter says words to the effect of; ‘This is how we brew it in Dublin,’ and there followed a recipe for Guinness!

The recipe for Guinness was, and for all I know still is, one of the most closely guarded industrial secrets in history. Gosset covers his backside later in the letter by saying something like, ‘Here, we have one or two additional procedures, but the recipe above is the essential method.’

I’ve never actually tried to follow the recipe as it is pretty laborious, involving making the malt from scratch rather than buying it in a big jar. However, seeing what I knew to be a legendary secret in cold print in a book which I’d casually pulled from the library shelf was quite an epiphany. I was like that other stout chap, Silent upon a peak in Darien.

Since then, whenever I teach students about the t-test, I break the ice with this story. In purely educational terms, this is a mistake, as thereafter they are no longer interested in the statistical method, they just want to know where they can find the book with the recipe for Guinness in it.

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Speaking of education, let me tell you a story, nothing to do with statistics or Guinness, which I heard from my sister Kathleen. Kath has taught history among other things at secondary schools. There was an assignment, I think for fourteen-year-old history students, in which they had first to read an extract from the memoirs of a German general from the nineteen-thirties. The extract dealt with a meeting in which a bunch of German top brass sat around the table and Hitler read out, in derisive tones, yet another letter from the allies telling him that he had better curtail his territorial expansion, or else there would be unspecified consequences. It became clearer and clearer from the fuhrer’s sarcastic tone that the ultimatum would be ignored and that territorial expansion would not only continue but accelerate. The writer of the memoir, evidently a man of some sense and decency, noted that as the intention to make further conquests became obvious, he grew more and more fearful.

After the passage, the students had to answer a number of questions to test their interpretation of this extract. One question was: ‘Why did the general become more and more fearful as the meeting went on?’

Kath recalls from marking the answers, that one student replied to this question with: ‘Because he was sitting beside Hitler.’