SAT Scores and Family Income
A debate is raging in the blogosphere about this graph, which shows that “Generally speaking, the wealthier a student’s family is, the higher the SAT score.”
Alex Tabarrok gets us up to speed on the debate thus far:
Greg Mankiw pointed out that the effect is unlikely to be purely causal because there may be an omitted variable bias, IQ for example. Paul Krugman and Matt Yglesias both attack Mankiw and point to graphs showing that income matters for college completion and enrollment, respectively, holding various achievement scores constant. Brad DeLong crunches the numbers on IQ and income correlation to estimate that half the effect is due to IQ and half to something else.
He says this doesn’t tell the whole story, though, “because there are a lot of ways that heredity/genes could explain the income/education correlation; IQ is only one possible mechanism, personality (e.g. conscientiousness) is another possibility.” He points to a longitudinal study of adopted children randomly assigned to parents which found no correlation at all between the income of the adopted parents and their adopted children.
While income didn’t matter, education did: “Having a college educated mother increases an adoptee’s probability of graduating from college by 7 percentage points, but raises a biological child’s probability of graduating from college by 26 percentage points.” Further, “The effect for father’s years of education is even larger; about a ten times larger effect on biological children than on adoptees.”
Obviously, this study (which I have not read beyond Tabarrok’s summary) raises other questions.
More likely higher income allows families to live in areas with better public schools or have the means to pay for private schools, allowing the children to have better all around education resulting higher test scores.
So let me get this straight, all of those parents that reduce hours worked to spend more time raising their children (whether it be taking off work completely or taking a job with less overtime demands and all points in-between), are doing the exact opposite of what they need to be doing for their kids to help them succeed?
I saw Dr. Mankiw’s post yesterday, considered writing one of my own in response to it, and then thought better of it. Dr. DeLong’s retort is right on the money.
Three things occur to me about the graphs above. First, a lot of things that influence income are heritable, either genetically, culturally, or due to the civil law. These include IQ, wealth, family connections, work ethic, attitudes toward education, whether the family eats dinner together, and so on. Many of these are not amenable to changing via the civil law. Doesn’t that constitute a powerful argument that the factors than can be controlled via the civil law should be to improve the prospects for the people at the low end of the spectrum?
Second, note that the graph at the top excludes all but those about a half standard deviation from the mean either way. There’s a reason for that: the graph doesn’t look nearly as good when you include those who are further outside the mean. Said another way if either IQ or SAT are meritocratic, they’re meritocratic within a very narrow range of results.
Third, again on the first graph, note that at all levels of income the orthogonality of the three scores is preserved, i.e. the lines don’t cross. That’s an artifact and not only is it an artifact but, since the mean scores in math and critical reading have, in fact, crossed over time (look it up) it suggests that there’s something wrong. It makes me suspicious about the both the test and the original article, generally.
http://www.christianpost.com/article/20090811/study-homeschoolers-scoring-well-above-public-school-peers/index.html
G. A. Phillips, are you familiar with the idea of selection bias?
Yup, evolution,global warming, abortion,Obama, remembering the deeds of T.K.. I understand not only the concept but have witnessed it in action.
Rich parents are probably rich because they’re smarter. Smarter parents have smarter kids. That’s not too complicated. (Although of course in the great Venn diagram of life, genetics, environment, free will and random chance all play their parts.)
That aside, tests are not terribly reliable. My daughter’s IQ just jumped by 20 points in a couple of months. High quality testing by professionals at both ends.
Why the jump? We put her in an extremely effective reading program. Did improved reading actually increase her IQ by 20 points? Of course not. It improved her test-taking ability.
In the SAT’s I tested out in the 99th percentile on English. (Fair enough, I am a writer.) But I also tested out in the 80th percentile in math. In reality I am functionally retarded at math. I top out at long division. I dropped out after 10th grade so I hadn’t even taken most of the math that was being tested.
Also did really well in the biology supplementary test. 90th percentile as I recall. How did I beat that test with literally no education in the subject? See 99th percentile in English: I get Latin and Greek root words.
Tests are mostly bullshit. Too bad they are the foundation of our educational system.
What I find most interesting is that this graph is interpreted as a problem that apparently needs to be addressed by driving the top more towards the mean. This is one of the more insidious implications of an emphasis on fairness.
But why is anyone surprised that people with more money, which generally implies more stable communities, more traditionally stable family structures, stronger support systems, and better schools do better over time?
More likely higher income allows families to live in areas with better public schools or have the means to pay for private schools, allowing the children to have better all around education resulting higher test scores.
You’ve got your causality inverted. Before the ETS stopped publishing inconvenient data, they allowed this data to be published. In 1995, the mean SAT scores of White children raised in families with incomes of less than $10,000 were 409V, 460M and the scores for Black children raised in families with incomes over $70,000 were 407V, 442M.
Clearly, being in a higher incomes class and going to better schools isn’t the primary factor responsible for increased SAT scores.
G. A. Phillips, are you familiar with the idea of selection bias?
If we posit that there is a relationship between the intelligence of the teacher and student academic achievement, then there will be a very large subset of the homeschooling sample where the intelligence of the parents is higher than that of the teachers. Using GSS data, Inductivist has come up with a rough estimate of mean high school teacher IQ – it has fallen from 107 to 104.
Rich parents are probably rich because they’re smarter. Smarter parents have smarter kids. That’s not too complicated.
You see, we can agree on some issues. However, your point about this not being too complicated obviously isn’t targeted at many on the left who adhere to the belief that environmental remediation has a powerful effect on human outcomes. As was noted at a Sociology conference “You don’t believe in DNA, do you?”
Doesn’t that constitute a powerful argument that the factors than can be controlled via the civil law should be to improve the prospects for the people at the low end of the spectrum?
Give it your best shot, what exactly are these factors which are proven to work at improving the prospects of students at the low end of the spectrum?
exactly,err, well i’ll use it as my point.Can I get a witness?
http://jessicassoapbox.blogspot.com/2007/03/bible-in-and-out-of-schools.html
Tests are mostly bullshit. Too bad they are the foundation of our educational system.
Is the concept of “mostly bullshit” in any way related to the notion of “mostly dead” that was espoused by Miracle Max? The SATI & SATII have greater predictive validity with respect to first year GPA than does High School GPA. So, if tests are “mostly bullshit”, then how would you describe course grading, “complete bullshit” perchance?
In fact, notice that the predictive validity of HSGPA was falling every year over the course of this study and that by 1999 the SATI alone had greater predictive validity than HSGPA.
A related issue here is the growing gender disparity in higher education, where female students are given an advantage because of their generally better HSGPA results while male students generally fair better at testing. A growing trend in higher education is to discount the more valid measurement, which favors boys, and put more emphasis on the less valid measurement, which favors girls.
“Give it your best shot, what exactly are these factors which are proven to work at improving the prospects of students at the low end of the spectrum?”
I am partial to the work of james Heckman. I would not expect you to be familiar with him, but he looks at this issue from the viewpoint of an economist. There is lots of neurocognitive research also available now. While IQ remains an important factor, it is not clear if it is even the most important factor anymore. Self-discipline, empathy (if you have an autistic kid you understand this one) and time management are probably just as important. Follows is a link to a good interview with Heckman. Please note that the Bell Curve book, the last book many conservatives ever read on the issue, only included those down to the age of 14.
http://www.minneapolisfed.org/publications_papers/pub_display.cfm?id=3278
Just a graf for fun follows. Most of us who have jobs and have observed management and fellow workers have figured most of this out anyway. The people running things are seldom the smartest. More often they are the hardest working or have the best people skills or are just the most ruthless.
Enriched early intervention programs targeted to disadvantaged children have had their biggest effect on noncognitive skills: motivation, self-control and time preference. We know that there’s a scientific basis for this finding. The prefrontal cortex, which is a center of these noncognitive skills, matures late. The executive function, the very definition of ourselves as people, the way we motivate ourselves, these things are malleable until quite late stages—into the 20s, according to research by neuroscientists. This means that in principle we can modify these behaviors. Noncognitive skills are powerfully predictive of a number of socioeconomic measures (crime, teenage pregnancy, education and the like) as I show in a recent paper with Jora Stixrud and Sergio Urzua.
Steve
I am partial to the work of james Heckman. I would not expect you to be familiar with him, but he looks at this issue from the viewpoint of an economist.
Never heard of the guy, but here’s something to consider, some dude wrote this in 1995:
Then, after actually studying the issue for a decade this same dude wrote this:
Note that:
1. he grants that IQ is a measure of cognitive ability
2. in fact, he uses IQ interchangeably with cognition and cognitive skill
3. he grants that IQ is not easily altered
4. he grants that it is important
His new tack: raise non-cognitive abilities. A laudable goal, but not what he set out to do one decade back. Remember, he set out this research program himself as the best hope for taking on the conclusions of Murray and Herrnstein though he granted many of their specific points (e.g. “Their empirical work substantiates the role of IQ in accounting for a considerable portion of ethnic differences in socioeconomic outcomesâ€).
While IQ remains an important factor, it is not clear if it is even the most important factor anymore.
It is the single most significant factor that has been identified. Yes, other factors are important, no one is denying that, but no other single factor has greater predictive validity in school success than IQ.
Please note that the Bell Curve book, the last book many conservatives ever read on the issue, only included those down to the age of 14.
Please note that heritability increases with age. This phenomenon explains why a good portion of the gains experienced in programs like Head Start are transitory.
You know, come to think of it, I do believe that I have heard of this Heckman fellow. Here is another paper he wrote, Labor Market Discrimination and Racial Differences in Premarket Factors:
GA:
You actually linked to that idiot screed with a straight face? tell me it was supposed to be funny.
Tango:
Of course none of this explains why wealth tracks with SAT’s, which was the original question.
But I can see you’re anxious to jump on the Murray hobby horse and ride it around the room a few times. So, consider this: the gap between whites and blacks is about the same as the gap between Jews and Asians on the one hand and white gentiles on the other.
Going by IQ alone it kind of seems as if non-Jewish white people, constituting as they do the single largest racial element in schools, are holding us back with their relatively poor performance.
But why stop with standardized tests? Why not expand our search for ability to other areas? In sports it’s quite clear that white people are inferior to pretty much everyone else.
In music and the arts again, it’s white people underperforming their numbers as a segment of the overall population.
In specific occupations — medicine, psychology, science generally, entertainment, law, banking — it’s clear that this would be a much wealthier and more successful country if we could use the miracles of modern science to somehow turn gentiles into Jews. I don’t know if mere religious conversion would accomplish this or not. Maybe we could conduct some tests — gentiles could be tested before and after a lecture on the Talmud delivered by a rabbi.
On the other hand, we’d definitely need some kind of DNA engineering to turn our caucasian brothers and sisters into asians. Perhaps a procedure that removed the “cauc” prefix would do it.
Going by IQ alone it kind of seems as if non-Jewish white people, constituting as they do the single largest racial element in schools, are holding us back with their relatively poor performance.
Michael, what do you suggest be done? We already know that Gentile Whites are the least represented demographic at Harvard and that Black students out represent them, when measured by proportion of study body in relation to national population. Are you suggesting that Gentile Whites be given the same preferences given to Blacks and Hispanics? I’m curious where you want to go with this.
But why stop with standardized tests? Why not expand our search for ability to other areas? In sports it’s quite clear that white people are inferior to pretty much everyone else.
There’s no reason to stop with standardized tests. Sure, expand our search for ability to other metrics. Go for it. Get back to me with some results on predictive validity of these alternative metrics. As for sports, should we implement special outreach programs and invest public monies to work towards the goal of equal outcomes?
Tell me more about this brave new world that you envision. How can we create equal outcomes for everyone?
Can you not see the smirk on my face————>
I am of a mind that people like this young girl are better then us(me and you)for what America was meant to be because the bible and it’s truth and laws are not missing from their respect or education.
If we go to the evidence that she sites it becomes obvious what the main problem is with educating the populace to live in a free and open society.
The IQ’s of rebellion for it’s own sake and the worldly condensations that we are seeped with are detrimental to the greater good of the way our society was set up in so many proving ways.
It should not be so hard for some one like you to see this overwhelming condition that we have put ourselves in by why of taking one book out of the system(classroom).
Tell me a better explanation.Ive heard them all and this is the only one that passes the test.
GA:
Where to begin? Let’s begin with your own education in critical thinking. It would be painfully easy to take this essay apart, but more time-consuming, so I’ll just pose some questions.
If it is true that the Bible improved education and its absence from schools caused education to suffer:
1) Why do Japan and Korea both have exemplary educational systems?
2) Why do American secular universities outperform American religious universities?
3) Why do the more religious sections of the country, principally the South, always underperform the dens of secularism in New England and the upper midwest?
4) Why do the most secular European countries not only outperform the US primary educational system, but more religious European systems?
5) Is it possible that other factors changed in this country since the 1950’s when the writer claims that the Bible was pushed out of education? For example, do you think fewer mothers are at home? Do you think we now test a broader slice of the demographic pie? Do you think society as a whole might have changed and those changes altered the schools? Do you think this woman is relying entirely on unquestioned assumptions based in nothing but sentimental and nostalgic reinterpretations of the past and equally distorted views of the present? Do you think it’s possible that we demand a great deal more of students now?
And on. And on. And seriously, it’s your own education that seems to be at issue here.
1) Why do Japan and Korea both have exemplary educational systems?
Because they’re peopled with Japanese and Koreans. If you’re trying to argue that these educational systems were isolated from Christian influence, then you’re flat out wrong. Jesuit missionaries were very active in setting up Japanese schools.
Christianity in Korea is quite pervasive:
2) Why do American secular universities outperform American religious universities?
1.) Secular universities outnumber religious universities so you’re going to see more hits and misses in the secular category. Notre Dame University or Georgetown University thoroughly outperform Florida International University.
2.) If you wish to argue some causal factor, then spell it out.
3) Why do the more religious sections of the country, principally the South, always underperform the dens of secularism in New England and the upper midwest?
As Senator Moynihan noted:
Anyone who knows US geography knows that New England and the Midwest, compared to the South, are closer to Canada.
4) Why do the most secular European countries not only outperform the US primary educational system, but more religious European systems?
Show us what you’re talking about here.
Tango:
?
I missed the part where I said anything about creating equal outcomes. Maybe you could point it out.
Mostly I was just yanking your chain.
Of course SAT predicts college GPA. Duh. GPA is test-dependent. So all you have here is that the ability to pass a test predicts an ability to pass tests. Kind of like saying the ability to jump really high today predicts the ability to jump really high a year later. It’s in the category of “no shit, Sherlock.”
If you create a system based almost entirely on one metric — standardized testing — it’s inevitable that tests become predictive. Unfortunately the tests don’t necessarily mean anything in terms of broader gauges of success.
A good SAT score leads to a good college GPA leads to Harvard leads to a fat law firm salary.
Just as in the days for which you seem to pine, white skin led to white schools led to white colleges led to white jobs. And black skin led to black schools which led directly to janitorial jobs. Thus “proving” the superiority of whites.
We have a system that begins by assuming the utility and importance of tests and then by refusing to examine its key assumption “proves” itself correct.
This is why more people should be required to take some philosophy courses. Honest to God, the drivel that passes for critical thinking.
We have a system that begins by assuming the utility and importance of tests and then by refusing to examine its key assumption “proves” itself correct.
This is why more people should be required to take some philosophy courses. Honest to God, the drivel that passes for critical thinking.
Thank you for this. I enjoyed it immensely. You’re a mine of comedy gold.
Tango:
People with minds half an inch wide always think it’s funny when someone suggests they open their minds a little. After all, what use would you have for anything that didn’t confirm your prejudices?
Kind of like testing itself: so long as you never question an assumption, you’re always right, aren’t you?
It’s too bad that humor loses its effect when you have to explain it.
The criticism: “We have a system that begins by assuming the utility and importance of tests and then by refusing to examine its key assumption “proves” itself correct.”
The humor: You assume that the system began by assuming the utility and importance of tests and when you criticize the system for refusing to examine its assumption you also fail to examine the assumption that this system just sprung into being with all of its assumptions untested.
That you were living in a glass house and casting stones was the comedy gold.
Tango:
Oy.
Honestly: just one epistemology class. Or you could read a book about it. It’s boring, I grant you, but it might help you. If you like I can send you something.
How did the testing advocates test their tests? With tests. See the small problem there?
No. Of course you don’t.
“1. he grants that IQ is a measure of cognitive ability
2. in fact, he uses IQ interchangeably with cognition and cognitive skill
3. he grants that IQ is not easily altered
4. he grants that it is important”
Yes. Heckman wrote one of the more intellectually honest criticisms of Murray’s book. However he sees it as most of the neuroscientists I read and know tend to see it, that it is just a beginning. We do not know all that much about IQ and cognition yet. We are still learning how children learn. When all is said and done IQ may be the single most important factor as you say, but the sum of those other factors may be more important. Maybe using achievement tests to measure IQ will yield to more refined tests telling us what we really want to know. Since what we really want to know is how well people can function, we may just find that IQ is necessary as a threshold event and that it is the non-cognitives that make the difference across very broad IQ levels. The military experience with test scores makes me lean this way.
Steve
Michael,
You present a very simple view of the world, a view predicated upon people being idiots and missing completely what is so obvious to you.
Test designers don’t validate their tests by relying on other tests. Only someone who knows nothing about the subject and is terribly taken with his own wisdom would assume that his exposure to a college philosophy class trumps the insights of those who know the subject material and underlying philosophical issues in more depth.
Let me give you a real world example:
In the above examples, the written test is not validated against other written tests, rather it is validated against performance in the field in a manner which measures importance to individuals and institutions. The Army finds that the written test has good predictive validity for soldier performance in the field.
Steve:
I think that’s right.
To go anecdotal here, I have two kids. One is a brilliant, tested IQ 150. The other is of average or slightly below average.
Guess which one can listen to and act effectively upon a multi-stage instruction such as “Do A, then B, and if C is the case, do D?”
Guess which one can almost instantly grasp a social situation and successfully enter the group and in fact, come to dominate the group?
Guess which one can operate independently without constant support and attention?
The answer to all three questions is: not the genius.
Tango:
You make this almost too easy:
Each situation you point to is a standardized test. None were under battlefield conditions. So again, what you’re testing with your tests is a test of test-taking ability which may, or may not, correlate to actual performance.
You suppose I could find any examples of soldiers who rated very highly on tests doing poorly when bad guys are shooting at their heads?
You think I might find a pilot or two who kicked ass on simulators but fell apart when the anti-aircraft missile was flying his way?
Do you suppose I could find any examples of soldiers who were poor at tests and performed well under the actual stress of combat?
Do you suppose there’s any chance that a company that produces tests and profits by that production would skew results to convince people of their accuracy?
Do you suppose it’s possible that what tests as intelligence is present alongside other factors that may not have been tested?
How smart do you think Alvin York was? You think maybe there were other, smarter guys in his unit who didn’t manage to singlehandedly capture a whole passel o’ krauts?
Who do you think was more intelligent, the Spartans or the Persians? A smart guy would have made a deal. Only a fucking idiot dies when he doesn’t have to.
And that’s just in the military world.
I say this as a guy who is 1) unbeatable on tests and as a consequence shows 2) a genius-level IQ: IQ is nothing but horsepower. It is useful, but it has its limits. IQ is not creativity. IQ is not courage. IQ is not originality. IQ is not resilience. IQ is not judgment. IQ is not moral force.
IQ is a measurement that appeals to people who have a high IQ but who lack that other characteristic that is also not IQ: wisdom.
Tango:
Long response caught in Joyner’s spam filter.
Short version: hah, nice try.
We do not know all that much about IQ and cognition yet.
We don’t know all that much about many things. Cancer, heart disease, various mental illnesses, climate, exposure to violence, etc, yet we still manage to improve processes even with limited knowledge. The same applies to what we know about intelligence, incomplete as that is.
When all is said and done IQ may be the single most important factor as you say, but the sum of those other factors may be more important.
I’m the classic moderate in this type of debate. I believe in the influence of genes and environment. I believe in the influence of intelligence and other behaviors. The extremists are the folks who believe that environment explains everything and genetics (or biology) explain nothing or that IQ is a fiction and all outcomes can be achieved simply by applying other environmental influences. Here is J.B. Watson, taking a “moderate” position:
Certainly other factors are important. We all likely know intelligent people who can’t exploit their intelligence to achieve success (assigning various, but common, definitions to the concept of success.) We also likely know of many people who are successful, in different fashions, who are not the brightest bulbs in the room.
Maybe using achievement tests to measure IQ will yield to more refined tests telling us what we really want to know.
I would say that what we want to know is whether these other factors can be taught, and if they can be taught will their influence diminish as the students get older and control more of their own environment. This was the heart of the problem with Head Start – so long as teachers could control the environment of the young students the students acted in ways that reflected what they had been taught. However, as the students got older they started taking more control of their own environments and weren’t so inclined to follow the teachings learned in Head Start, the gains evaporated.
Teaching perseverance, or diligence, or fostering a competitive or cooperative attitude, in students can certainly yield desired results in the classroom if the taught behaviors can be implemented. These behaviors can be implemented when the teachers have control over the students. The trick is to see whether the behaviors will stick and whether the students, following their own volition, will behave in the desired fashion.
This brings me back to my earlier question to Dave, what factors exactly are known to work.
Since what we really want to know is how well people can function, we may just find that IQ is necessary as a threshold event and that it is the non-cognitives that make the difference across very broad IQ levels.
I agree with this, with the proviso that threshold levels will vary across fields and that IQ will, once beyond the threshold level, also have some influence on performance. In other words, once we’re beyond the IQ threshold there are multiple paths towards success, some paths cross easy terrain while other paths cross difficult terrain.
Harry, did you just look at the picture of the young woman and make your judgment.
And I don’t think you grasp the evidence that rules 4, 5 and 12 don’t work on me, I don’t care about them, or any of the others for that matter, but, you guessed it, I don’t have a problem using them against you.
Not to mention abortions, did I mention abortions?
How about suicides?
Rap,lol??
Tecno??
Liberals control the system were this comes from.
I know I was there.
And I answered your questions but it got stuck in the spam filter, plus it funner to watch TangoMan crush you with statistically clear reasoning.
Ya it’s suck I know, all I got is the high school diploma I had to go and test out of at the local technical collage because I was a liberal dropout,plus I dint have to take math after 7th grade because I had all the credits for high school and my teacher comes in and says you don’t have to take math anymore because of this and I was happy and dint(i don’t remember my mechanics but can still do most of what I need in my head, go figure, I tried hard to kill off them brain cells, Hard!!!).The thousands of books Ive read, speed reader<—–got a b+ in that class because I was in a jail school release program at the time and liked to spend some classes getting high.
But I did manage a Triple PH D’s in D@D, f–king up, and talking Sh-t,a 30 day program certificate or two and a world wide bible telecasters diploma.
But enough about me I libgress……
@TangoMan
It is difficult in the extreme for many, many people to accept this argument:
Blacks are intellectually inferior to whites as measured by IQ tests. And this inferiority is not a matter of socio-economic deprivation, but is a matter of primordial, genetic fact. Therefore, any attempt to remediate the station of blacks in our society by attention to socio-economic conditions is doomed because it runs up against the genetic wall.
The question is, then, if that argument is correct, are we not faced with a permanent genetically determined underclass? A class coextensive with race? How to deal with this?
And wisdom comes from where?
The question is, then, if that argument is correct, are we not faced with a permanent genetically determined underclass? A class coextensive with race? How to deal with this?
It’s important to keep in mind that individuals are not wholly defined by the groups to which they belong. While it’s true that the mean IQ level of Blacks is 85 (no one familiar with the field disputes this finding, what is disputed is the cause) there are plenty of individuals, in fact 7 million, which IQs higher than the Caucasian mean of 100.
That said, your questions are important ones. Do we deal with the world as it is and try to formulate policies which reflect our principles and respond to reality, or do we try to form a world of make believe and then formulate policies which reflect our principles and hope they can work in the world of make believe. For example, look at the world view underlying the No Child Left Behind legislation. This legislation is anchored in a world view lifted from Lake Woebegone, where every child is seen as above average. The legislation calls for 100% proficiency rates of tested students by 2013-2014 and it will penalize those schools which fail to bring about the impossible. How exactly is it a better choice to implement a policy that has a 100% certainty of failure and how is it better to blame countless people for bringing about that failure compared to a policy which views the world realistically?
Is it really better to spin a society’s wheels in pursuit of unachievable ends in a process predicted upon a false understanding of reality? I don’t think so. Therefore, I favor broader discussion on how society should deal with the reality we do find.
Another example – similar to the Heckman finding above, which found that the Hispanic-White wage gap disappears once test scores were controlled, the same finding is found in the Black-White wage gap:
Is it better to acknowledge reality or is it better to falsely accuse people of horrendous racism based on a false view of reality?
Retort, I don’t think that word means what you think it means. DeLong just said the same thing Mankiw did, but with more precision. If Mankiw read DeLong’s post I don’t think he’d disagree with it. Mankiw isn’t saying there is no correlation between income and test scores, but that its isn’t a univariate process. Mankiw is saying,
Test Scores = F(X) not,
Test Scores = F(income).
Income could be one component of the vector X, but focusing solely on income would bias your results if the true model is the first one. From a stastical modelling stand point it as an almost banal point.
Well, unless you are Krugman or Yglesias.
Now that’s funny coming from the guy who argued from his own personal views to the general population. And then of course denied it. Keep going Michael, you’re are most amusing.