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Using Math to make Guinness

William Sealy Gosset, statistician and rebel | Picture from Wikimedia Commons

Let me tell you a story about William Sealy Gosset. William was a Chemistry and Math grad from Oxford University in the class of 1899 (they were partying like it was 1899 back then). After graduating, he took a job with the brewery of Arthur Guinness and Son, where he worked as a mathematician, trying to find the best yields of barley.

But this is where he ran into problems.

One of the most important assumptions in (most) statistical tests is that you have a large enough sample size to create inferences about your data. You can’t make many comments if you only have 1 data point. 3? Maybe. 5? Possibly. Ideally, we want at least 20-30 observations, if not more. It’s why when a goalie in hockey, or a batter in baseball, has a great game, you chalk it up to being a fluke, rather than indicative of their skill. Small sample sizes are much more likely to be affected by chance and thus may not be accurate of the underlying phenomena you’re trying to measure. Gosset, on the other hand, couldn’t create 30+ batches of Guinness in order to do the statistics on them. He had a much smaller sample size, and thus “normal” statistical methods wouldn’t work.

Gosset wouldn’t take this for an answer. He started writing up his thoughts, and examining the error associated with his estimates. However, he ran into problems. His mentor, Karl Pearson, of Pearson Product Moment Correlation Coefficient fame, while supportive, didn’t really appreciate how important the findings were. In addition, Guiness had very strict policies on what their employees could publish, as they were worried about their competitors discovering their trade secrets. So Gosset did what any normal mathematician would.

He published under a pseudonym. In a startlingly rebellious gesture, Gosset published his work in Biometrika titled “The Probable Error of a Mean.” (See, statisticians can be badasses too). The name he used? Student. His paper for the Guinness company became one of the most important statistical discoveries of the day, and the Student’s T-distribution is now an essential part of any introductory statistics course.

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Sabremetrics and Math: How sports can teach statistics

Statistics.

Math.

Mental arithmatic.

Do those words scare you? If they do, you’re in good company. Mathematical anxiety is a well studied phenomenon that manifests for a number of different reasons. It’s an issue I’ve talked about before at length, and something that frustrates me no end. In my opinion though, one of the biggest culprits behind this is how math alienates people. Lets try an example:

If the average of three distinct positive integers is 22, what is the largest possible value of these three integers?
A: 64
B: 63
C: 33
D: 42
E: 48

Too easy? How about this one:

The average of the integers 24, 6, 12, x and y is 11. What is the value of the sum x + y?

A: 11
B: 17
C: 13
D: 15

I do statistics regularly, and I find these tricky. Not because the underlying math is hard, or that they’re fundamentally “difficult,” but because you have to read the question 3 or 4 times just to figure out what they’re asking. This is exacerbated at higher levels, where you need to first understand the problem, and then understand the math.*

Last week, my colleague Cristina Russo discussed how sports can be used to teach biology. Today I’m going to discuss a personal example, and how I use sports to explain statistics.

One of my main objectives as a statistics instructor is to take “fear” out of the equation (math joke!), and make my students comfortable with the underlying mathematical concepts. I’m not looking for everyone to become a statistician, but I do want them to be able to understand statistics in everyday life. Once they have mastered the underlying concepts, we can then apply them to new and novel situations. Given most of my students are athletically minded or have a basic understanding of sports, this is a logical and reasonable place to start.

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Mathematical Literacy: A necessary skill for the 21st century

Abacus

My Grade 9 math teacher was a jolly British man, and probably taught me one of the most useful things I ever learnt in high school: how to do basic math in my head (or, since I was in the British educational system, it was Grammar School). Every so often we’d go into our math class and find little bits of paper on every desk. This was a harbinger of doom – it meant we were having a 20 question surprise quiz. And not just any quiz, a mental arithmetic quiz. He would read a question out loud twice, and then we’d have to do the math. He’d give us some leeway (you didn’t have to be exact), but man did I ever hate those quizzes. At the time, they seemed impractical and a colossal waste of time. In retrospect, they were incredibly useful.

Now, being on the other side of the divide, I see something that concerns me. I regularly TA undergraduate and graduate students in statistics, and I notice that many of them, while they have all the skills to do math, are absolutely terrified of it. And as soon as you fear a subject, or don’t want to learn it, you won’t. Your mind will shut down and every instinct you have will prevent you from engaging in the material. As a result, I spend the first hour of any class I’m teaching talking to the students and determining what it is they don’t understand to tailor my sessions accordingly. But the comments generally involve variations on:

“I just don’t get math.”
“I’ve never been any good at math.”
“I don’t like it.”

Of these, the first two concern me. The third I can’t help – I don’t need my students to love math, but I do want them to understand enough to pass the course and feel comfortable interpreting statistical analyses. There’s a culture among schoolkids to dislike math and the perception that it’s largely useless. While in chemistry you can see stuff blow up, and in biology you can dissect animals, math is a largely abstract concept. That perception then manifests as a lack of interest, which results in poorer performance, and that puts people off math.

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