Feb 27, 2013

The XL-Files: A Fundamental Link between Statistics and Humor


Contributing Editor Xiao-Li Meng writes:

My new year’s reading started with a holiday gift: On the Money, a collection of over 400 cartoons in The New Yorker from 1925–2009. No, after months of learning about fundraising, money was least alluring on a day when my alarm clock took a rest. But I could use a few laughs, even at my own expense or with irony. Indeed, the gift was from an alumna, and I wondered if it was meant to be a friendly reminder: relax, don’t take money (and your job) too seriously.

However I did end up taking the book very seriously, reading it word by word. Huh? Reading cartoons? Of course not. But there is an introduction by Malcolm Gladwell, whose name might not be as familiar to statisticians as the title of one of his best-sellers: Outliers (and perhaps also The Tipping Point and Blink). Gladwell’s philosophical introduction also started with irony. As a writer for The New Yorker, he considered the book very strange, “because we are a magazine for people for whom money is a secondary concern. … So what on earth does The New Yorker think about when we think about money?” Regardless of your opinions about his characterization, his short answer was, “we make jokes about it.”

Gladwell’s long answer began with an anecdote of how stunned he was at a corporate retreat, when a CFO used a business-like PowerPoint presentation to tell his life story. It ended with the key point: “People who want the world to conform to the principles of business are Realists. People who think the other way around—this is true whether they spend their days parsing sonnets or actuarial tables—are Romantics, and the Romantic position … is the comic position.”

Gladwell’s main supporting example is a statistical one. Bernard Madoff’s fund had a 96% “winning” percentage, with “annual gains that fell like clockwork between 10–12 percent.” Why didn’t he mimic the volatility of a hedge fund, with a more enticing long-run gain and a much less suspicious winning pattern? Gladwell’s answer is that it is “because Madoff understood what consistency means in personal terms: it means trustworthiness, mastery, competence, safety.” It was precisely this consistency that convinced Harry Markopolos, Madoff’s bête noire, that Madoff was really a Made-up. As Markopolos argued in his 17-page memo to the SEC, “No major league baseball hitter bats .960, no NFL team has ever gone 96 wins and only four losses over a 100-game span, and you can bet everything you own that no money manager is up 96 percent of the months, either.” In other words, when we take a Realist’s position, Madoff’s made-up consistency points us to exactly the opposite conclusion it had aimed to achieve, that is, he is completely untrustworthy.

By no means is this example meant to glorify the Realists’ position. As Gladwell emphasized: “The victims of Bernie Madoff would have done well to think of Madoff in business terms, not personal terms. Then again, the traders at AIG, who have cost taxpayers many, many multiples of what Madoff cost the world, would have done well to import a healthy dose of personal virtue into their professional practices.”

Despite the painful context, Gladwell’s underlying message inspired me to think about a fundamental link between statistics and humor. The discipline of statistics is essentially about separating commonalities (e.g., patterns, signals) from individualities (e.g., variability, noise). In contrast, the best kind of humor is often the result of judiciously mixing commonalities and individualities to create comic effect.

A story told by Rick Cleary (visiting Harvard from Bentley) at our 2008 holiday party, illustrates this point well. At the end of the last lecture of an introductory course for which he was a teaching assistant, the professor (the late George Casella—whose obituary appears here) encouraged the class to ask any remaining questions on anything that had been covered. A student who had never asked any question before raised her hand. “Professor Casella, I really enjoyed your class, but there is one thing that has puzzled me for the entire semester. Why are standard deviations always six?”

You will be laughing now, or in a few seconds, if you are a real statistician. Otherwise you would be laughing at how nerdy statisticians must be if they can find humor in the number six. What makes this story greatly humorous to statisticians is the mixing of a well-understood commonality (standard deviation is commonly denoted by $σ$) and an unexpected individuality (the student’s mistaking $σ$ for 6). It would not be humorous at all if six were replaced by one because George, for whatever reason, decided to use the letter l for standard deviation in his course.

What could be a more joyful way to celebrate the International Year of Statistics than by telling the world that Statistics is the most enjoyable profession on earth, because along with every depressing study or erroneous argument there is an enticing recipe for entertaining ourselves?

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