Gee Whiz

November 28, 2007
Posted by Jay Livingston

Some time ago, the comments on a post here brought up the topic of the “gee whiz graph.” Recently, thanks to a lead from Andrew Gelman , I’ve found another good example in a recent paper.

The authors, Leif Nelson and Joseph Simmons, have been looking at the influence of initials. Their ideas seem silly at first glance (batters whose names begin with K are more likely to strike out), like those other name studies that claim people named Dennis are more likely to become dentists while those named Lawrence or Laura are more likely to become lawyers

But Nelson and Simmons have the data. Here’s their graph showing that students whose last names begin with C and D get lower grades than do students whose names begin with A and B.

The graph shows an impressive difference, certainly one that warrants Nelson and Simmon’s explanation:
Despite the pervasive desire to achieve high grades, students with the initial C or D, presumably because of a fondness for these letters, were slightly less successful at achieving their conscious academic goals than were students with other initials.

Notice that “slightly.” To find out how slight, you have to take a second look at the numbers on the axis of that gee-whiz graph. The Nelson-Simmons paper doesn’t give the actual means, but from the graph it looks as though the A students’ mean is not quite 3.37. The D students average between 3.34 and 3.35, closer to the latter. But even if the means were, respectively, 3.37 and 3.34, that’s a difference of a whopping 0.03 GPA points.

When you put the numbers on a GPA axis that goes from 0 to 4.0, the differences look like this.
According to Nelson and Simmons, the AB / CD difference was significant (F = 4.55, p < .001). But as I remind students, in the language of statistics, a significant difference is not the same as a meaningful difference.

Worlds in Collision

November 26, 2007
Posted by Jay Livingston

There’s been a lot written about how the Internet has shifted the boundary of private and public. People are willing to put more of their lives out there in cyberspace– most notably on networking sites like MySpace and Facebook – assuming, for some reason, that only their friends will have the ability or interest to stop and look.

But cyberlore teems with cautionary tales of the wrong people getting the wrong information. A prospective employer sees what a job candidate has put on his MySpace page and finds it much different from the picture the candidate presented in his resumé and interview. It’s the problem Goffman called “audience segregation.” We don’t present quite the same self to each group that we interact with – employers and drinking buddies, for example – and we do our best to make sure that the audiences for these different performances don’t overlap. Jeremy Freese closed down his blog because of this problem. (I can’t remember the specifics.)

It had all been academic for me till one night last week. My son was looking at Facebook, and looking over his shoulder I noticed that one of his “friends ” was a kid I’d known since they were in kindergarten together. I wanted to see a larger version of the postage-stamp size picture. No dice, Dad. He logged out.

So remembering that I had a Facebook account (though I never use it), I logged in on my laptop, and started looking through friends on my son’s page. My wife, too, was curious about these kids. My son, of course, was mortified. I couldn’t get to his actual page with his “wall” and other information. But I could scroll through the pages of his Facebook friends.
We both felt uncomfortable. He had always known that anyone in the world could view that list of friends, but he hadn’t really considered this possibility of his parents seeing it.

“This is not good,” he said. “Worlds are colliding.”

Execution and Deterrence

November 20, 2007
Posted by Jay Livingston

The Sunday New York Times had a front page article about recent studies showing that the death penalty deters murder. The studies, nearly all done by economists, give estimates of between 3 and 18 lives saved for each person executed.

The main critique of these studies argues that the small number of executions makes it impossible to draw solid conclusions. Last year, for example, Arizona had no executions; this year, Arizona executed one person. A change of 3 or even 18 murders in the next year, would probably fall within the range of random change.

In many areas of life, it makes sense to play the percentages. You send a left-handed batter against a right-handed pitcher. Even if the strategy doesn’t work this time, there’s no great consequence, and it will work in the long run thanks to the “law of large numbers” (what most people know as the “law of averages”). But , as the name says, that law is enforced only when the numbers are large. Do we want the numbers of executions to be that large?

Personally, when it comes to killing prisoners, I’d prefer a demonstration of deterrence that works with small numbers. I want to see a clearer link between cause and effect. Ideally, we would have evidence of at least three actual Arizonans (preferably 18) who were deterred by that execution. But of course we don’t have such evidence. All we have are estimates from complicated multiple regressions based on decades of data.

I don’t have the data sets or the statistical skills to do these regressions, so I did my own quick and dirty, highly nonscientific analysis of a couple of states – Texas and Oklahoma. In 1996, for example, the number of executions in Texas dropped from 19 to 3. The number of murders should have skyrocketed. But the next year, the number of murders decreased by 150 (from 1477 to 1327).

Then W. and Alberto got back to work, and in 1997, executions went from 3 to 37. Let’s see, at 10 saved lives per execution, murder in the next year should have been down by at least three hundred. But in fact, the next year, there were 20 more murders.

The numbers from Oklahoma, which started emulating its neighbor to the south, are similarly inconclusive. In 2000, it increased executions by 5 (from 6 to 11). Were there fifty or even fifteen fewer murders the next year? No, the number went from 182 to 185.

Yes, my method (or is it my methodolgy?) stinks. Its estimate of lag time is crude. It leaves out all those other factors that might affect murder rates, and it ignores the aggregate data. But when it comes to the state taking lives, I’m inclined to demand something that works every time, not just “in general.”

The economists’ formulations also leave out something important – a model of just how deterrence works. They simply make the standard economic assumption that raising the cost of something lowers demand. If you raise the cost of committing murder, fewer people will be willing to pay that price.

But before I accept the idea that deciding whether to kill someone is like deciding whether to buy a new car, I’d like to see some street-level evidence.

Finally, none of this speaks to other issues raised in the Times article and in the letters responding to it – the costs (especially relative to other anti-crime policies), the morality, and the risk of executing the innocent.

Buffett's Bet

November 18, 2007
Posted by Jay Livingston

Often, a simple example is the best way to get a point across.

For example, the US tax system is incredibly complicated. To illustrate the idea that it also favors the wealthy, Warren Buffett (the second richest man in the country) has said that he pays a lower rate of income tax than does his secretary. Buffett’s income was about $47 million last year, and he paid about 18% in federal income taxes. His employees, whose incomes ranged from $60,000 to $750,000, paid an average of 33%.

It’s anecdotal evidence of course, so Buffett has extended it to the Forbes 400 – Forbes Magazine’s list of the 400 wealthiest Americans. He’s offered to bet any of them one million dollars that they paid a lower income tax rate than did their office secretaries and receptionists.

A few of them have responded, and Forbes online prints what they have to say.
  • Philip Ruffin ($2.1 billion) said that Buffett is “senile.”
  • Kenneth Fisher ($1.8 billion) said, “He should stick to his area of expertise. It’s a little late to be trying to learn and teach social policy.”
  • Randal J. Kirk ($1.6 billion) said, “His thesis here seems grossly simplistic.”
As my father said many years ago as we listened to some politician’s “denial” of some charge made by an opponent, “He called him a son-of-a-bitch, but he didn’t call him a liar.”

These guys called Buffett names (senile, simplistic), but none of them took Buffett’s offer of the million-dollar bet.

John Catsimatidis ($2.1 billion) said, “The numbers can fool you . . . . I have a complex business . . . I own real estate, stocks and bonds, and so I have depreciation and write-offs.” Which is precisely Buffett’s point. The tax system favors rich people for the way they make their money, and it punishes people who work for a weekly paycheck.