Justice Scalia Does the Math

March 25, 2008
Posted by Jay Livingston

Supreme Court Justice Antonin Scalia. Even those who disagree with him speak of his brilliance, his incisive intelligence, and his wit. Apparently, he does better on the verbal part than on the math. An article by Adam Liptak in the New York Times today nails it. In an opinion upholding a death penalty conviction, Scalia dismisses the problem of wrongful convictions because they constitute such a minuscule fraction of cases. For support, he cites the number: “Between 1989 and 2003, the authors identify 340 ‘exonerations’ nationwide—not just for capital cases, mind you, nor even just for murder convictions, but for various felonies.” (Note that Scalia puts exonerations in quotation marks. He still thinks the dudes are guilty.) Then he quotes approvingly from a prosecutor.

[L]et’s give the professor the benefit of the doubt: let’s assume that he understated the number of innocents by roughly a factor of 10, that of 340 there were 4,000 people in prison who weren’t involved in the crime in any way. During that same 15 years, there were more than 15 million felony convictions across the country. That would make the error rate .027 percent—or, to put it another way, a success rate of 99.973 percent.

Most students in the undergraduate methods course could tell you what’s wrong with this fraction. Exonerations are rare because they require extraordinary legal effort, efforts that prosecutors and often judges strongly resist. Claims of innocence in any but the most serious cases don’t get that kind of effort. And most of those 15 million felony convictions are not for the more serious degrees of murder and rape. So the 4,000 in the numerator of the fraction is almost certainly a severe undercount of all wrongful convictions. For the denominator, however, Scalia takes all felony convictions in the US. He’s using either a wrong numerator or a wrong denominator, or both. For an analogy, Liptak quotes Samuel Gross in a forthcoming article in Annual Review of Law and Social Science:

By this logic we could estimate the proportion of baseball players who’ve used steroids by dividing the number of major league players who’ve been caught by the total of all baseball players at all levels: major league, minor leagues, semipro, college, and little league – and maybe throwing in football and basketball players as well.

I’ll try to remember this example the next time I teach about stat and methods. Or courts. Or the next time I read about Scalia’s incisive intelligence.

To the Moon, Winston

March 22, 2008
Posted by Jay Livingston

One-third of British kids surveyed said that Winston Churchill was the first man to walk on the moon. The British press is having a field day with this colorful item. (I mean, “The British press are having a field day with this colourful bit.”). Here’s how the Times played it:

March 20, 2008

Winston Churchill was first to walk on the Moon, say children

Lucy Bannerman

Winston Churchill: leader, victor, and, according to a third of schoolchildren, astronaut. The most celebrated British Prime Minister of the 20th century was the first man to walk on the Moon, one in three young people told a survey.

The black hole in their knowledge was revealed after an online poll asked 1,400 children, aged from 6 to 14, some basic astronomical questions.

Not only did a significant number confuse Neil Armstrong with the statesman who led the Allies to victory . . . .

Seems like there’s less here than meets the eye. An online survey doesn’t give you a representative sample, nor do we know how many of these kids were in the younger side of the distribution. Would we wring our hands if a lot of US 6-10 year olds didn’t know who FDR was?

I also wonder how the question was asked. Was it “Who was Winston Churchill?” with moonwalker as one of the distractors? Since the survey was mostly about astronomy, this would be a reasonable choice for those younger kids who didn’t know who he was. What would a 1940s PM be doing in an astronomy quiz anyway?

Or was it “Who was the first man to walk on the moon?” with Churchill as one of the choices. If you’re eight years old and you don’t know the answer, you might go for a name that sounds vaguely familiar.

The story also reveals some interesting things about what Times writers “know.” They know, for instance, that a black hole is a gap or an absence of matter and not a powerful magnetic gravitational field that sucks in everything.*

They also know for a fact that Churchill was the person who “led the Allies to victory.” No ethnocentrism here, right? But my schoolteachers told me that Ike played that role. And Russians no doubt were taught that it was Stalin.

*I once heard a Boston Celtic, in a post-game offhand comment, say that Kevin McHale in the low post was “a black hole – once the ball goes in there, it never comes back out.” Apparently, Times writers know less about astronomy than do NBA jocks.

Mi Casa But Not Su Casa

March 21, 2008
Posted by Jay Livingston

Not exactly “it depends on what the meaning of is is,” but relevant to the problem of constructing questions. Andrew Gelman posted this a few days ago.

When preparing our GSS survey questions on social and political polarization, one of our questions was, “How many people do you know who have a second home?” This was supposed to help us measure social stratification by wealth– we figured people might know if their friends had a second home, even if they didn’t know the values of their friends’ assets. But we had a problem – a lot of the positive responses seemed to be coming from people who knew immigrants who had a home back in their original countries.

Put that in your pipe and use it in your methods class.

I’ve been phone-surveyed (not by the GSS), and several times I have asked the interviewer what some part of a question meant. The response was usually, in so many words, “Hey, I didn’t write these questions. I just get paid $6.50 an hour to read ’em.” OK, I would think, but I know that my answer doesn’t mean what your employers think it means.

Ivan Dixon

March 20, 2008
Posted by Jay Livingston

A few years ago, I was stuck in a motel room one morning. My son,14, was flipping through the TV channels and hit upon a Twilight Zone marathon on F/X or Sci-Fi. The episode when we turned on the TV had only about ten minutes left, but at once I realized, in some Twilight Zonish dejà vu way, that I had seen this episode long ago when I was fourteen. It was about a small-time boxer at the end of his career, a man facing the reality of the limitations of his life. Not the sort of thing that a kid would understand, certainly not a kid like me. The twilight of a career was not the “twilight” that the the show had in mind. On the contrary, the message of this episode, delivered by a young boy who looks up to the fighter, is that he should believe in the impossible and keep boxing.

But there was something about the performance, the way the actor conveyed the sense of exhaustion and acceptance. Here was a man, a real grown-up, coming to grips with the realities of his life and his situation. That was the message that came through, not the call to ignore reality and live in the fictional Zone. The actor’s performance transcended the silliness of the scripted plot, making the character so real that I still remembered him decades later.*

BOLIE: You know, a fighter don’t need a scrapbook, Henry. You want to know what he’s done and where he’s fought? You read it in his face. He's got the whole story cut into his flesh. St. Louis, 1949. Guy named Sailor Leavitt. A real fast boy. And this, Memorial Stadium. Syracuse, New York. Italian boy. Fought like Henry Armstrong. All hands and arms, just like a windmill on the wind. . . .

The actor was Ivan Dixon, who died Sunday.

I never saw him in Hogan’s Heros, but I did see “Nothing But a Man” when it was released. I didn’t recognize him then as the boxer I had seen on The Twilight Zone just a few years earlier. That realization didn't happen until decades later in a motel room in western Massachusetts.

If you haven’t seen “Nothing But a Man,” you should rent and watch it immediately. If you teach sociology, you should use it in class – for what it says about race in the US, for what it says about how social arrangements affect the interior life of marriages and of individuals. You should watch it for the performances by Dixon, Abbey Lincoln (who doesn't sing a note), Yaphet Kotto and others.

When I first saw “Nothing But a Man,” I thought it was the best black-themed film I’d ever seen. I still do.

* Another blogger has linked to the Twilight Zone episode on YouTube. If you want to see it, you can find it here.