Steven Dubner - Freakonomics
From this jumble, he must determine which factors are correlated and which are not.
In the case of the ECLS data, it might help to think of regression analysis as performing the following task: converting each of those twenty thousand schoolchildren into a sort of circuit board with an identical number of switches.
Each switch represents a single category of the child’s data: his first-grade math score, his third-grade math score, his first-grade reading score, his third-grade reading score, his mother’s education level, his father’s income, the number of books in his home, the relative affluence of his neighborhood, and so on.
Now a researcher is able to tease some insights from this very complicated set of data. He can line up all the children who share many characteristics—all the circuit boards that have their switches flipped the same direction—and then pinpoint the single characteristic they don’t share. This is how he isolates the true impact of that single switch on the sprawling circuit board. This is how the effect of that switch—and, eventually, of every switch—becomes manifest.
Let’s say that we want to ask the ECLS data a fundamental question about parenting and education: does having a lot of books in your home lead your child to do well in school? Regression analysis can’t quite answer that question, but it can answer a subtly different one: does a child with a lot of books in his home tend to do better than a child with no books? The difference between the first and second questions is the difference between causality (question 1) and correlation (question 2). A regression analysis can demonstrate correlation, but it doesn’t prove cause. After all, there are several ways in which two variables can be correlated. X can cause Y; Y can cause X; or it may be that some other factor is causing both X and Y. A regression alone can’t tell you whether it snows because it’s cold, whether it’s cold because it snows, or if the two just happen to go together.
The ECLS data do show, for instance, that a child with a lot of books in his home tends to test higher than a child with no books. So those factors are correlated, and that’s nice to know. But higher test scores are correlated with many other factors as well. If you simply measure children with a lot of books against children with no books, the answer may not be very meaningful. Perhaps the number of books in a child’s home merely indicates how much money his parents make. What we really want to do is measure two children who are alike in every way except one—in this case, the number of books in his home—and see if that one factor makes a difference in his school performance.
It should be said that regression analysis is more art than science. (In this regard, it has a great deal in common with parenting itself.) But a skilled practitioner can use it to tell how meaningful a correlation is—and maybe even tell whether that correlation does indicate a causal relationship.
So what does an analysis of the ECLS data tell us about school-children’s performance? A number of things. The first one concerns the black-white test score gap.
It has long been observed that black children, even before they set foot in a classroom, underperform their white counterparts. Moreover, black children didn’t measure up even when controlling for a wide array of variables. (To control for a variable is essentially to eliminate its influence, much as one golfer uses a handicap against another. In the case of an academic study such as the ECLS, a researcher might control for any number of disadvantages that one student might carry when measured against the average student.) But this new data set tells a different story. After controlling for just a few variables—
including the income and education level of the child’s parents and the mother’s age at the birth of her first child—the gap between black and white children is virtually eliminated at the time the children enter school.
This is an encouraging finding on two fronts. It means that young black children have continued to make gains relative to their white counterparts. It also means that whatever gap remains can be linked to a handful of readily identifiable factors. The data reveal that black children who perform poorly in school do so not because they are black but because they tend to come from low-income, low-education households. A typical black child and white child from the same socioeconomic background, however, have the same abilities in math and reading upon entering kindergarden.
Great news, right? Well, not so fast. First of all, because the average black child is more likely to come from a low-income, low-education household, the gap is very real: on average, black children still are scoring worse. Worse yet, even when the parents’ income and education are controlled for, the black-white gap reappears within just two years of a child’s entering school. By the end of first grade, a black child is underperforming a statistically equivalent white child.
And the gap steadily grows over the second and third grades.
Why does this happen? That’s a hard, complicated question. But one answer may lie in the fact that the school attended by the typical black child is not the same school attended by the typical white child, and the typical black child goes to a school that is simply…bad. Even fifty years after Brown v. Board, many American schools are virtually segregated. The ECLS project surveyed roughly one thousand schools, taking samples of twenty children from each. In 35 percent of those schools, not a single black child was included in the sample. The typical white child in the ECLS study attends a school that is only 6 percent black; the typical black child, meanwhile, attends a school that is about 60 percent black.
Just how are the black schools bad? Not, interestingly, in the ways that schools are traditionally measured. In terms of class size, teachers’ education, and computer-to-student ratio, the schools attended by blacks and whites are similar.
But the typical black student’s school has a far higher rate of troublesome indicators, such as gang problems, nonstudents loitering in front of the school, and lack of PTA funding. These schools offer an environment that is simply not conducive to learning.
Black students are hardly the only ones who suffer in bad schools. White children in these schools also perform poorly. In fact, there is essentially no black-white test score gap within a bad school in the early years once you control for students’ backgrounds. But all students in a bad school, black and white, do lose ground to students in good schools. Perhaps educators and researchers are wrong to be so hung up on the black-white test score gap; the bad-school/good-school gap may be the more salient issue. Consider this fact: the ECLS data reveal that black students in good schools don’t lose ground to their white counterparts, and black students in good schools outperform whites in poor schools.
So according to these data, a child’s school does seem to have a clear impact on his academic progress. Can the same be said for parenting? Did all those Baby Mozart tapes pay off? What about those marathon readings of Goodnight Moon?
Was the move to the suburbs worthwhile? Do the kids with PTA parents do better than the kids whose parents have never heard of the PTA?
The wide-ranging ECLS data offer a number of compelling correlations between a child’s personal circumstances and his school performance. For instance, once all other factors are controlled for, it is clear that students from rural areas tend to do worse than average. Suburban children, meanwhile, are in the middle of the curve, while urban children tend to score higher than average. (It may be that cities attract a more educated workforce and, therefore, parents with smarter children.) On average, girls test higher than boys, and Asians test higher than whites—although blacks, as we have already established, test similarly to whites from comparable backgrounds and in comparable schools.
Knowing what you now know about regression analysis, conventional wisdom, and the art of parenting, consider the following list of sixteen factors. According to the ECLS data, eight of the factors show a strong correlation—positive or negative—with test scores. The other eight don’t seem to matter. Feel free to guess which are which.
The child has highly educated parents.
The child’s family is intact.
The child’s parents have high socioeconomic status.
The child’s parents recently moved into a better neighborhood.
The child’s mother was thirty or older at the time of her first child’s birth.
The child’s mother didn’t work between birth and kindergarten.
The child had low birthweight.
The child attended Head Start.
The child’s parents speak English in the home.
The child’s parents regularly take him to museums.
The child is adopted.
The child is regularly spanked.
The child’s parents are involved in the PTA.
The child frequently watches television.
The child has many books in his home.
The child’s parents read to him nearly every day.
Here now are the eight factors that are strongly correlated with test scores:
• The child has highly educated parents.
• The child’s parents have high socioeconomic status.
• The child’s mother was thirty or older at the time of her first child’s birth.
• The child had low birthweight.
• The child’s parents speak English in the home.
• The child is adopted.
• The child’s parents are involved in the PTA.
• The child has many books in his home.
And the eight that aren’t:
• The child’s family is intact.
• The child’s parents recently moved into a better neighborhood.
• The child’s mother didn’t work between birth and kindergarten.
• The child attended Head Start.
• The child’s parents regularly take him to museums.
• The child is regularly spanked.
• The child frequently watches television.
• The child’s parents read to him nearly every day.
Now, two by two:
• Matters: The child has highly educated parents.
• Doesn’t: The child’s family is intact.
A child whose parents are highly educated typically does well in school; not much surprise there. A family with a lot of schooling tends to value schooling.
Perhaps more important, parents with higher IQs tend to get more education, and IQ is strongly hereditary. But whether a child’s family is intact doesn’t seem to matter. Just as the earlier-cited studies show that family structure has little impact on a child’s personality, it does not seem to affect his academic abilities either. This is not to say that families ought to go around splitting up willy-nilly.
It should, however, offer encouragement to the roughly twenty million American schoolchildren being raised by a single parent.
• Matters: The child’s parents have high socioeconomic status.
• Doesn’t: The child’s parents recently moved into a better neighborhood.
A high socioeconomic status is strongly correlated to higher test scores, which seems sensible. Socioeconomic status is a strong indicator of success in general—
it suggests a higher IQ and more education—and successful parents are more likely to have successful children. But moving to a better neighborhood doesn’t improve a child’s chances in school. It may be that moving itself is a disruptive force; more likely, it’s because a nicer house doesn’t improve math or reading scores any more than nicer sneakers make you jump higher.
• Matters: The child’s mother was thirty or older at the time of her first child’s birth.
• Doesn’t: The child’s mother didn’t work between birth and kindergarten.
A woman who doesn’t have her first child until she is at least thirty is likely to see that child do well in school. This mother tends to be a woman who wanted to get some advanced education or develop traction in her career. She is also likely to want a child more than a teenage mother wants a child. This doesn’t mean that an older first-time mother is necessarily a better mother, but she has put herself—and her children—in a more advantageous position. (It is worth noting that this advantage is nonexistent for a teenage mother who waits until she is thirty to have her second child. The ECLS data show that her second child will perform no better than her first.) At the same time, a mother who stays home from work until her child goes to kindergarten does not seem to provide any advantage. Obsessive parents might find this lack of correlation bothersome—
what was the point of all those Mommy and Me classes?—but that is what the data tell us.
• Matters: The child had low birthweight.
• Doesn’t: The child attended Head Start.
A child who had a low birthweight tends to do poorly in school. It may be that being born prematurely is simply hurtful to a child’s over-all well-being. It may also be that low birthweight is a strong forecaster of poor parenting, since a mother who smokes or drinks or otherwise mistreats her baby in utero isn’t likely to turn things around just because the baby is born. A low-birthweight child, in turn, is more likely to be a poor child—and, therefore, more likely to attend Head Start, the federal preschool program. But according to the ECLS
data, Head Start does nothing for a child’s future test scores. Despite a deep reservoir of appreciation for Head Start (one of this book’s authors was a charter student), we must acknowledge that it has repeatedly been proven ineffectual.
Here’s a likely reason: instead of spending the day with his own undereducated, overworked mother, the typical Head Start child spends the day with someone else’s undereducated, overworked mother. (And a whole roomful of similarly needy children.) As it happens, fewer than 30 percent of Head Start teachers have even a bachelor’s degree. And the job pays so poorly—about $21,000 for a Head Start teacher versus $40,000 for the average public-school kindergarten teacher—
that it is unlikely to attract better teachers any time soon.
• Matters: The child’s parents speak English in the home.
• Doesn’t: The child’s parents regularly take him to museums.
A child with English-speaking parents does better in school than one whose parents don’t speak English. Again, not much of a surprise. This correlation is further supported by the performance of Hispanic students in the ECLS study.
As a group, Hispanic students test poorly; they are also disproportionately likely to have non-English-speaking parents. (They do, however, tend to catch up with their peers in later grades.) So how about the opposite case: what if a mother and father are not only proficient in English but spend their weekends broadening their child’s cultural horizons by taking him to museums? Sorry. Culture cramming may be a foundational belief of obsessive parenting, but the ECLS
data show no correlation between museum visits and test scores.
• Matters: The child is adopted.
• Doesn’t: The child is regularly spanked.
