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Flip it around

Mark Palko discusses a radio interview on the effect of parents on children’s education. In short, the interviewer (Stephen Dubner of Freakonomics fame) claims that the research shows that parents don’t have much influence on whether their children go to college. The evidence is based on a comparison of adopted and non-adopted children. Palko makes a convincing case that the statistical analysis (by economist Bruce Sacerdote) doesn’t show what Dubner says it shows.

I looked over the linked transcript, and overall I’m less unhappy than Palko is about the interview. I agree that some of the causal implications are sloppy, and I think it’s a bit silly for the interviewer (Kai Ryssdal) to use celebrities as a benchmark. (Ryssdal says, “if [a certain parenting style is] good enough for Steven Levitt, it’s good enough for me.” But Levitt is a multimillionaire—he’ll always have a huge financial cushion. It’s not clear that what works for him would work for others who are not so well situated.)

But, taking the interview as a whole, I’m happy with its quantitative tone. And the findings that were presented there, even if they don’t tell the whole story, they are informative and interesting in their own right. These are not factoids or cherry-picked statistics that Dubner is presenting, they’re interesting research findings.

This example interests me for three reasons.

First, at the level of statistics and social science, it’s an interesting challenge to estimate effects of families and to try to understand the contributions of nurture and nature. This is a much-discussed topic (although, as Palko explains, this doesn’t stop people from getting confused over it), and I won’t discuss it further here.

Second, the example interests me in the connections between the science and the politics. As a conservative, Dubner is happy to see evidence confirming the idea that kids who don’t go to college, don’t go because of their genes rather than because they’re not on a college track. This makes educational inequality (and related economic inequalities) seem more like facts of nature than something that society could do something about (for example, through taxation). In contrast, this sort of data won’t make Dubner so comfortable:

Among the top-scoring quartile of students on the SAT: 80% of high-SES students went on to a four-year college, compared to only 44% of low-SES students.

Among the top-scoring students who do go to college, 80% of the high-SES kids graduate, compared to 45% of the kids of low socio-economic status.

Third–and this is the point I want to focus on here–this example illustrates hidden assumptions and is an excellent case to demonstrate one of my favorite tricks for understanding statistical patterns.

What is this trick? I call it “flipping it around.”

Recall that statistics is all about comparisons. The trick is, instead of comparing A to B, compare B to A.

For example, “WInning the Nobel Prize adds two years to your lifespan” becomes “Not getting the Nobel Prize reduces your expected lifespan by two years.” Which emphasizes the comparison that’s being done.

I thought of this here because of this bit from that radio interview:

Dubner: If you’re a child who’s adopted into a high-education family — that is where the parents both went to college — you are about 16 percentage points more likely to go to college than a kid who gets adopted into a low-education family. So that sounds pretty good, OK?

Dubner follows up by arguing that 16% isn’t really so much (a claim that Palko disputes), but that’s not relevant for my discussion here. What I want to focus on is: is it a good thing if children adopted into high-education families are much more likely to go to college, compared to children adopted into low-education families?

Let’s flip it around.

Taking the study’s results as correct, if you’re a child who’s adopted into a low-education family you are about 16 percentage points less likely to go to college than a kid who gets adopted into a high-education family.

Got that? Just for being adopted into the wrong kind of family, your chance of going to college goes down by 16%! That doesn’t sound so good now, does it? Which makes you wonder why Dubner was so sure that the +16% effect (which of course is the same thing, just looked at from the other direction) sounded so good.

I’m not attributing any malice to Dubner here. I just think this happens all the time, that people look at a comparison without thinking of it in the opposite direction.

P.S. Just to emphasize: I’m not trying to stake out any position on education policy or anything like that here. I’m just using this example to illustrate the perhaps surprising benefits that can be gained by “flipping it around.”

P.P.S. Given the relative audience sizes, I must be one of the very few people to have heard of this from Palko’s blog and not from the radio!

5 Comments

  1. Andy says:

    I listened to the Freakonomics podcast in question, and I think when Dubner said the 16% effect was “pretty good” he wasn’t really talking about the results for adopted kids. He was saying that this is perhaps encouraging news for parents who want to have a nonbiological impact on their kids’ success.

  2. Steve Sailer says:

    And keep in mind that the worst adoptive family is, typically, not so bad. I’m adopted, and my adoptive parents were carefully checked out by professionals for all the usual major flaws, such as alcoholism, criminal record, poverty, shaky employment, marital instability, etc. Consequently, I had a very nice, stable upbringing. So, restriction of range is a problem with interpreting adoption studies.

  3. Bruce Sharp says:

    Love the idea of “flipping” to better understand statistics. I often rely on a similar reversal to determine whether or not someone’s stated motivations are genuine. For example, consider hackers: Many claim that they break into computers because they’re concerned about computer security, and by publicizing vulnerabilities, they’re improving security. Sounds sorta plausible… but what happens when you reverse it? Don’t ask, “Why would a person break into a computer?” Ask: “How would a person make a computer more secure?” They’d write firewalls. They’d write intrusion detection algorithms and forensic tools. They wouldn’t write SQL Slammer.

  4. Michael W. says:

    Re the SAT statistics: Many conservatives argue (eg ‘Bell Curve’) that SES is predominantly caused by IQ differences, which (they claim) is a strictly heritable trait, hence environmental factors are still mostly irrelevant. Of course, the major flaw is in confusing heritability with inheritance, but enough has already been written about that elsewhere.