These data concern school choice, an issue that most people feel strongly about in one direction or another. True believers of school choice argue that their tax dollars buy them the right to send their children to the best school possible. Critics worry that school choice will leave behind the worst students in the worst schools. Still, just about every parent seems to believe that her child will thrive if only he can attend the right school, the one with an appropriate blend of academics, extracurriculars, friendliness, and safety.

School choice came early to the Chicago Public School system. That’s because the CPS, like most urban school districts, had a disproportionate number of minority students. Despite the U.S. Supreme Court’s 1954 ruling in Brown v. Board of Education of Topeka, which dictated that schools be desegregated, many black CPS students continued to attend schools that were nearly all-black. So in 1980 the U.S. Department of Justice and the Chicago Board of Education teamed up to try to better integrate the city’s schools. It was decreed that incoming freshmen could apply to virtually any high school in the district.

Aside from its longevity, there are several reasons the CPS school-choice program is a good one to study. It offers a huge data set—Chicago has the third-largest school system in the country, after New York and Los Angeles—as well as an enormous amount of choice (more than sixty high schools) and flexibility. Its take-up rates are accordingly very high, with roughly half of the CPS students opting out of their neighborhood school. But the most serendipitous aspect of the CPS program—for the sake of a study, at least—is how the school-choice game was played.

As might be expected, throwing open the doors of any school to every freshman in Chicago threatened to create bedlam. The schools with good test scores and high graduation rates would be rabidly oversubscribed, making it impossible to satisfy every student’s request.

In the interest of fairness, the CPS resorted to a lottery. For a researcher, this is a remarkable boon. A behavioral scientist could hardly design a better experiment in his laboratory. Just as the scientist might randomly assign one mouse to a treatment group and another to a control group, the Chicago school board effectively did the same. Imagine two students, statistically identical, each of whom wants to attend a new, better school. Thanks to how the ball bounces in the hopper, one goes to the new school and the other stays behind. Now imagine multiplying those students by the thousands. The result is a natural experiment on a grand scale. This was hardly the goal in the mind of the Chicago school officials who conceived the lottery. But when viewed in this way, the lottery offers a wonderful means of measuring just how much school choice—or, really, a better school—truly matters.

So what do the data reveal?

The answer will not be heartening to obsessive parents: in this case, school choice barely mattered at all. It is true that the Chicago students who entered the school-choice lottery were more likely to graduate than the students who didn’t—which seems to suggest that school choice does make a difference. But that’s an illusion. The proof is in this comparison: the students who won the lottery and went to a “better” school did no better than equivalent students who lost the lottery and were left behind. That is, a student who opted out of his neighborhood school was more likely to graduate whether or not he actually won the opportunity to go to a new school. What appears to be an advantage gained by going to a new school isn’t connected to the new school at all. What this means is that the students—and parents—who choose to opt out tend to be smarter and more academically motivated to begin with. But statistically, they gained no academic benefit by changing schools.

And is it true that the students left behind in neighborhood schools suffered? No: they continued to test at about the same levels as before the supposed brain drain.

There was, however, one group of students in Chicago who did see a dramatic change: those who entered a technical school or career academy. These students performed substantially better than they did in their old academic settings and graduated at a much higher rate than their past performance would have predicted. So the CPS school-choice program did help prepare a small segment of otherwise struggling students for solid careers by giving them practical skills. But it doesn’t appear that it made anyone much smarter.

Could it really be that school choice doesn’t much matter? No self-respecting parent, obsessive or otherwise, is ready to believe that. But wait: maybe it’s because the CPS study measures high-school students; maybe by then the die has already been cast. “There are too many students who arrive at high school not prepared to do high school work,” Richard P. Mills, the education commissioner of New York State, noted recently, “too many students who arrive at high school reading, writing, and doing math at the elementary level. We have to correct the problem in the earlier grades.”

Indeed, academic studies have substantiated Mills’s anxiety. In examining the income gap between black and white adults—it is well established that blacks earn significantly less—scholars have found that the gap is virtually eradicated if the blacks’ lower eighth-grade test scores are taken into account. In other words, the black-white income gap is largely a product of a black-white education gap that could have been observed many years earlier. “Reducing the black-white test score gap,” wrote the authors of one study, “would do more to promote racial equality than any other strategy that commands broad political support.”

So where does that black-white test gap come from? Many theories have been put forth over the years: poverty, genetic makeup, the “summer setback” phenomenon (blacks are thought to lose more ground than whites when school is out of session), racial bias in testing or in teachers’ perceptions, and a black backlash against “acting white.”

In a paper called “The Economics of ‘Acting White,’” the young black Harvard economist Roland G. Fryer Jr. argues that some black students “have tremendous disincentives to invest in particular behaviors (i.e., education, ballet, etc.) due to the fact that they may be deemed a person who is trying to act like a white person (a.k.a. ‘selling-out’). Such a label, in some neighborhoods, can carry penalties that range from being deemed a social outcast, to being beaten or killed.” Fryer cites the recollections of a young Kareem Abdul-Jabbar, known then as Lew Alcindor, who had just entered the fourth grade in a new school and discovered that he was a better reader than even the seventh graders: “When the kids found this out, I became a target . . . It was my first time away from home, my first experience in an all-black situation, and I found myself being punished for everything I’d ever been taught was right. I got all A’s and was hated for it; I spoke correctly and was called a punk. I had to learn a new language simply to be able to deal with the threats. I had good manners and was a good little boy and paid for it with my hide.”

Fryer is also one of the authors of “Understanding the Black-White Test Score Gap in the First Two Years of School.” This paper takes advantage of a new trove of government data that helps reliably address the black-white gap. Perhaps more interestingly, the data do a nice job of answering the question that every parent—black, white, and otherwise—wants to ask: what are the factors that do and do not affect a child’s performance in school?

In the late 1990s, the U.S. Department of Education undertook a monumental project called the Early Childhood Longitudinal Study. The ECLS sought to measure the academic progress of more than twenty thousand children from kindergarten through the fifth grade. The subjects were chosen from across the country to represent an accurate cross section of American schoolchildren.