September 7, 2007

Occam's Razor

You need three graphs to explain how education works in the U.S.

The first graph tells us about the students.



The data comes from the National Longitudinal Study of Youth.

This is our raw material. By far the most important variable affecting the inputs of education is IQ. Simply put, it's far easier to educate a smart kid than it is to educate a dim kid. The sad reality for the low IQ kids is that IQ is a brutal predictor of academic success.

In the U.S. the mean IQ is about 100. We know how to educate the kids with IQs above about 100, at least at the K-12 level. The kids on the left half, not so much.

There are thousands of schools in the U.S., each teaching a little differently. However, the results are almost always the same: the kids on the right succeed and the kids on the left fail. This is because most of the differences aren't instructionally significant. (I'm ignoring for the purposes of this discussion the handful of specialized programs that are capable of improving the educational outcomes of elementary school students because there is little hard data for the upper grades.)

IQ isn't the entire story when it comes to academic outcomes, but it is a major factor. There are lots of other environmental factors that affect academic performance. These factors have a distribution like IQ. So to give an extreme case, the kid with the 95 IQ with the good work ethic and parental support may perform better than the kid with the 105 IQ with behavioral problems and dyslexia.

Now that we know about our student inputs, we have to recognize that kids are not evenly distributed in society. Kids live with their parents, usually in a house that their parents pay for. Typically, parents buy or rent in the best neighborhood they can afford which is largely determined by their socio-economic status.

Graph 2 shows us how children's mean IQ is distributed according to parental SES. The parents with the high SES tend to have the children with the highest mean IQ, while the parents with the lowest SES tend to have children with the lowest mean IQ.

This is why schools located in affluent suburbs perform better than schools in poor areas and perform much better than schools located in the inner city. If an affluent suburban school is pulling most of its students from an area where the parental SES falls within the 7th to 10th decile, you can see how the white kids will have mean IQs in the 110-115 range. Even the black kids in that school district will have higher IQs than the average black kid, though these kids will tend to have lower IQs than the average white student. (This explains the disparity in scores that I highlighted for Radnor Middle School in my last post.)

You should also be able to see why a poor rural school comprised mostly of white kids will tend to have students with a below-average mean IQ. And, this also explains why poor inner city schools comprised mostly of black and Hispanic students is going to be full of students with extremely low mean IQs. At best, these schools will only have about 20% of its students with IQs over 100. And remember what I wrote about us not knowing how to educate kids below IQs of 100.

This is why NCLB cares about the subgroup data for blacks, Hispanics and poor students in affluent suburban schools.

Which brings us to the third and final graph. The third graph is a scatter plot of the academic performance of Pennsylvania's 501 school districts as a function of Parental SES.


As you can see, the results are exactly what you'd predict from the first two graphs. The schools from high parental SES areas with kids having a higher mean IQ tend to perform better, while the schools from low parental SES areas with kids having a lower mean IQ tend to perform worse. (I'm not going to post the graph that plots academic performance vs. instructional spending which shows a very low correlation.)

The schools falling below the regression line are under-performing. The schools falling above the regression line are over-performing. I've highlighted (white arrows) two clusters of schools. The first group of slightly over-performing schools is located at about the $27k point. The second group of slightly under-performing schools is located at about the $67k point. Notice how the academic performance of the over-performing cluster is below the performance of the under-performing cluster. Under NCLB, the under-performing schools would likely to be labeled as success stories, while the over-performing schools would likely be labeled as failures.

I don't mean to imply that schools shouldn't be doing a better job or that there isn't lots of room for improvement. They should be and there is. The point of this post is to highlight the reality that most schools in poor areas aren't doing all that poorly and the affluent suburban schools aren't doing all that well once you consider the hand they've been dealt.

We need to start approaching education with Occam's razor instead of Occam's butterknife if we expect to fix NCLB.

13 comments:

CrypticLife said...

Great post, Ken. Analyzing school performance should be based on what they get coming in versus what they produce coming out. The teachers are right that once a year testing isn't the best evaluation method.

To really get at the effect of particular teachers, you'd want to do a pre-test and post-test. Then it's just a matter of designing the tests and calculating how much the students improved. I would think if I were a teacher I'd want to do this myself, or if I were designing standards for a state I'd try to implement this.

Anonymous said...

Good god, man!

Don't you know that Charles Murray was crucified for saying something similar in the Bell Curve.

KDeRosa said...

I'm trying to stick to the less controversial parts of the bell curve, the parts that the APA has endorsed.

4trogan said...

I don't buy it.

I don't buy that the main reason kids perform well or poorly is because of their IQ being the biggest predictor.

Those high IQ, higher SES kids aren't performing better mostly by virtue of their IQs (on a collective basis) -- they are performing better because their higher IQ, higher paid parents can spot trouble in their academic performance, and moreover, are in a position to do something about it by either helping out at home, affording tutoring, or knowing their rights and pestering the school for additional help.

THIS is what is not happening in the lower SES neighborhoods, because if the lower SES neighborhood parents did with their kids what the high SES neighborhood parents were doing? Yeah, the high poverty schools would be doing just as good.

As much as I abhor blaming student achievement (usually the lack thereof) on the parents (which the public schools love to do), I do feel it is true that the successs of schools can be attributed to the parents -- even though the duty to educate surely rests with the public school.

Ulitmately, what your data suggest to me is that Johnny will do well if he has a parent to make sure it happens -- because one can NOT, in any way, rely on the school to do its job.

KDeRosa said...

I disagree.

There are plenty of identical twin studies that disprove your theory. The studies \show that a child's biological IQ is more important than other environmental factors, such as parental support. Placing a low IQ with a high IQ family unfortunately does not get you high IQ performance.

sailorman said...

Ken,

If you are claiming that the I.Q. is not the product of environment, then referring to the graph in your post, you are claiming that the races differ significantly in I.Q.

Remember "The Bell Curve?" That book advanced the racial-difference-in-I.Q. argument as well. Those theories have been fairly well debunked, I think.

KDeRosa said...

Sailorman,

I'm sticking to the non-controversial parts of the Bell Curve, the parts endorsed by the APA:

* IQ scores have high predictive validity for individual differences in school achievement.

*IQ scores have predictive validity for adult occupational status, even when variables such as education and family background have been statistically controlled.

*Individual differences in intelligence are substantially influenced by both genetics and environment.

*There is little evidence to show that childhood diet influences intelligence except in cases of severe malnutrition.

IQ seems to have both a genetic and an environmental component. Nonetheless, while not completely immutable, IQ is difficult to raise by attempting to change the various environmental factors that are commonly thought to affect IQ.

No reasonable person believes that the IQ gap doesn't exist. And, it doesn't even matter what these IQ tests are actually measuring. Whatever it is they are measuring correlates highly with academic perforamance regardless of the presence of lack of all the other environmental factors that affect academic performance.

4trogan said...

Ken said:

"I disagree. There are plenty of identical twin studies that disprove your theory. The studies \show that a child's biological IQ is more important than other environmental factors, such as parental support. Placing a low IQ with a high IQ family unfortunately does not get you high IQ performance."

Well, we all love Engelmann, and in his book "Your Child Can Succeed" he sets about explaining how all of those twin studies have the twins in similar SES environments. When the twins are reared in disparate environments, IQs are disparate.

In fact, Engelmann is a known proponent that IQ is nurture, not nature. Barring a disabling condition, I agree.

sailorman said...

KDeRosa said...

Sailorman,

I'm sticking to the non-controversial parts of the Bell Curve, the parts endorsed by the APA:

* IQ scores have high predictive validity for individual differences in school achievement.

Sure. That's because of how I.Q> tests are designed.

*IQ scores have predictive validity for adult occupational status, even when variables such as education and family background have been statistically controlled.
Again, no surprise here.

*Individual differences in intelligence are substantially influenced by both genetics and environment.
1) Define "substantial."
2) Acknowledge that race is not, actually, genetic in the sense discussed here. The tendency of a particular individual to self-classify as, or be classified as, "black" or "caucasian" says essentially zero about their genetic makeup.

*There is little evidence to show that childhood diet influences intelligence except in cases of severe malnutrition.
No particular debate here. Although this would probably be quite difficult to test; there may be an effect we can't see yet.

IQ seems to have both a genetic and an environmental component.
Yes. But GENETIC =\ RACIAL.

Nonetheless, while not completely immutable, IQ is difficult to raise by attempting to change the various environmental factors that are commonly thought to affect IQ.
This is true. You cannot easily raise a control group of whites who are subject to racism, nor a control group of blacks who are not.

No reasonable person believes that the IQ gap doesn't exist.
OK, that's an annoying statement, as well as an ad hom.

We're not discussing whether the I.Q. gap exists, we're discussing why it exists. And (haven't gotten there yet) whether it's an accurate measure.

And, it doesn't even matter what these IQ tests are actually measuring. Whatever it is they are measuring correlates highly with academic performance regardless of the presence of lack of all the other environmental factors that affect academic performance.
This I may agree with. Can you elaborate more?

TangoMan said...

1) Define "substantial."

-MRI-based studies estimate a moderate correlation between brain size and intelligence of 0.40 to 0.51
- g is significantly linked to differences in the volume of frontal grey matter, which are determined primarily by genetic factors... the volume of frontal grey matter has additional predictive validity for g even after the predictive effect of total brain volume is factored out
- Only one region is consistently activated during three different intelligence tasks when compared to control tasks...The surface features of the tasks differed (spatial, verbal, circles) but all were moderately strong predictors of g (g LOADING; range of r, 0.55–0.67), whereas control tasks were weaker predictors of g (range of r, 0.37–0.41). Neural activity in several areas, measured by a positron emission tomography (PET) scan, is greater during high-g than low-g tasks.
- Speed and reliability of neural transmission are related to higher intelligence. Early neuroimaging studies using PET found that intelligence correlated negatively with cerebral glucose metabolism during mental activity leading to the formulation of a 'neural efficiency' hypothesis...

Acknowledge that race is not, actually, genetic in the sense discussed here. The tendency of a particular individual to self-classify as, or be classified as, "black" or "caucasian" says essentially zero about their genetic makeup.

Thanks for the advice, but no thanks. I'll stick with studies like this:

What makes the current study, published in the February issue of the American Journal of Human Genetics, more conclusive is its size. The study is by far the largest, consisting of 3,636 people who all identified themselves as either white, African-American, East Asian or Hispanic. Of these, only five individuals had DNA that matched an ethnic group different than the box they checked at the beginning of the study. That's an error rate of 0.14 percent.

According to Neil Risch, PhD, a UCSF professor who led the study while he was professor of genetics at Stanford, the findings are particularly surprising given that people in both African-American and Hispanic ethnic groups often have a mixed background. "We might expect these individuals to cross several different genetic clusters," Risch said. This is especially true for Hispanics who are often a mix of Native American, white and African-American ancestry. But that's not what the study found. Instead, each self-identified racial/ethnic group clumped into the same genetic cluster.

For each person in the study, the researchers examined 326 DNA regions that tend to vary between people. These regions are not necessarily within genes, but are simply genetic signposts on chromosomes that come in a variety of different forms at the same location.

Without knowing how the participants had identified themselves, Risch and his team ran the results through a computer program that grouped individuals according to patterns of the 326 signposts. This analysis could have resulted in any number of different clusters, but only four clear groups turned up. And in each case the individuals within those clusters all fell within the same self-identified racial group.

"This shows that people's self-identified race/ethnicity is a nearly perfect indicator of their genetic background," Risch said.


This is true. You cannot easily raise a control group of whites who are subject to racism, nor a control group of blacks who are not.

No, but you can take a large group of Korean orphaned babies and randomly place them in American families which span the socioeconomic spectrum and study them. After they've been raised as Americans you can then tease out the environmental and genetic factors as they manifest in the adult lives of the adoptees. The children's height, BMI, and income are highly correlated to genetics. The children were compared to the children born to the adoptive parents, and while there as a positive correlation between the SES of the parents and the income earned by the natural born children, the adoptive children had an essentially flat line. Furthermore, the Korean adoptees incomes had a higher correlation to the Korean American mean than to the SES of the homes they were raised in or to the incomes of the adopted siblings.

If one posits that family environment is key to academic success then we can control family attitudes to education as we compare educational outcomes across race. This is exactly what As Stanley Sue and Sumie Okazaki did in their paper Asian American Educational Achievements: A Phenomenon in Search of an Explanation where they found that the parenting styles and values found in East Asian-American homes tend to correlate with lower test scores when they are found in white homes.

Anonymous said...

http://www.edge.org/q2006/q06_3.html

STEVEN PINKER
Psychologist, Harvard University; Author, The Blank Slate

Groups of people may differ genetically in their average talents and temperaments

The year 2005 saw several public appearances of what will I predict will become the dangerous idea of the next decade: that groups of people may differ genetically in their average talents and temperaments.

* In January, Harvard president Larry Summers caused a firestorm when he cited research showing that women and men have non-identical statistical distributions of cognitive abilities and life priorities.

* In March, developmental biologist Armand Leroi published an op-ed in the New York Times rebutting the conventional wisdom that race does not exist. (The conventional wisdom is coming to be known as Lewontin's Fallacy: that because most genes may be found in all human groups, the groups don't differ at all. But patterns of correlation among genes do differ between groups, and different clusters of correlated genes correspond well to the major races labeled by common sense. )

* In June, the Times reported a forthcoming study by physicist Greg Cochran, anthropologist Jason Hardy, and population geneticist Henry Harpending proposing that Ashkenazi Jews have been biologically selected for high intelligence, and that their well-documented genetic diseases are a by-product of this evolutionary history.

* In September, political scientist Charles Murray published an article in Commentary reiterating his argument from The Bell Curve that average racial differences in intelligence are intractable and partly genetic.

Whether or not these hypotheses hold up (the evidence for gender differences is reasonably good, for ethnic and racial differences much less so), they are widely perceived to be dangerous. Summers was subjected to months of vilification, and proponents of ethnic and racial differences in the past have been targets of censorship, violence, and comparisons to Nazis. Large swaths of the intellectual landscape have been reengineered to try to rule these hypotheses out a priori (race does not exist, intelligence does not exist, the mind is a blank slate inscribed by parents). The underlying fear, that reports of group differences will fuel bigotry, is not, of course, groundless.

The intellectual tools to defuse the danger are available. "Is" does not imply "ought. " Group differences, when they exist, pertain to the average or variance of a statistical distribution, rather than to individual men and women. Political equality is a commitment to universal human rights, and to policies that treat people as individuals rather than representatives of groups; it is not an empirical claim that all groups are indistinguishable. Yet many commentators seem unwilling to grasp these points, to say nothing of the wider world community.

Advances in genetics and genomics will soon provide the ability to test hypotheses about group differences rigorously. Perhaps geneticists will forbear performing these tests, but one shouldn't count on it. The tests could very well emerge as by-products of research in biomedicine, genealogy, and deep history which no one wants to stop.

The human genomic revolution has spawned an enormous amount of commentary about the possible perils of cloning and human genetic enhancement. I suspect that these are red herrings. When people realize that cloning is just forgoing a genetically mixed child for a twin of one parent, and is not the resurrection of the soul or a source of replacement organs, no one will want to do it. Likewise, when they realize that most genes have costs as well as benefits (they may raise a child's IQ but also predispose him to genetic disease), "designer babies" will lose whatever appeal they have. But the prospect of genetic tests of group differences in psychological traits is both more likely and more incendiary, and is one that the current intellectual community is ill-equipped to deal with.

Anonymous said...

Oops.

This is the post I meant to cite as politically incorrect.

Do you think a major newspaper would ever publish such an op-ed?

Perhaps the media's refusal to broadcast such opinions helps explain why the public doesn't understand that high income suburban schools are just as bad at instruction as low income urban ones?

KDeRosa said...

Lots of good comments.

Anon, you are, of course, right.

We'd also get a lot fewer inane articles like this.