The Bell Curve

[_Analytics]

Do the people who score a 5 on the AP marh test have a "g" higher than the people who only score a 2 or 3? Maybe (probably?), but the correlation between AP test scores and IQ test scores will be closer to zero than to 0.75.

That's my opinion. If you are aware of actual research that demonstrates I'm wrong about that, I'd love to read it.

I think that's the wrong comparison. The people who take the AP calc exam are already people for the the most part who think they have reason to believe they can pass it. You don't get a lot of people who struggle with high school Algebra taking the AP calc exam.

What I'm suggesting is that passing AP Calc exams would be predictive of higher IQ as converted from college preparation exam score because college preparation exams test the ability to take math tests well and this is a significant part of the overall score. Since math isn't the sole part of the exam, you have to be careful about extending beyond this point.

I'm sure people who pass the bar exam have high IQs too. That doesn't change the fact that it is an achievement test, not a cognitive test.

I don't think you need incredibly high general intelligence to have calculus down, but if you are measuring someone's intelligence with a test that asks average level high school math problems, you're going to get higher scores, much higher even, out of people who do well in calculus.

According to researchers, the people who do well in calculus would have gotten much higher scores on these tests before they took calculus, and that taking calculus would have little affect on their IQ score.

I don't think the math problems on the SAT are exactly the same thing as "average level high school math problems," though. Although the problems often require some basic algebra, for the most part they aren't testing whether you've mastered Algebra I. Rather, they are testing whether you can solve cognitive puzzles--some of which are tricky--that happen to be expressed in terms of Algebra I formulas and relationships. Knowing how to calculate the volume of a bowl using double-integrals won't necessarily help you solve a tricky Algebra I problem in 90 seconds.

Just to remind you of what we are talking about, I happened to come across the following at the New York Times:

Scores on the SAT correlate very highly with scores on standardized tests of intelligence, and like IQ scores, are stable across time and not easily increased through training, coaching or practice. SAT preparation courses appear to work, but the gains are small — on average, no more than about 20 points per section.

All I'm doing is thinking that this guy happens to know what the research says on such things. I don't have a dog in the fight other than my opinion that the correlation that Dr. Hambrick says exist really do exist. If you have evidence that he is wrong please share it.

If you think that quality of schooling has nothing to do with how well you do in calculus or the math that gets you to calculus, there's no problem here outside of failure to explain why we spend so much money trying to squeeze out better performance. If you do, then that's obviously in conflict with the belief that quality of schooling does not matter much to college preparation exam performance.

I've repeatedly said that the reason why you want a good calculus teacher is so that you'll do well in calculus. That answer doesn't click with you because you seem to think mastering calculus is a huge boost to your IQ.

[_Analytics]

I guess it comes down to how one views race as a construct. If it's shorthand for something that has more to do with outward appearance and the way we group people based on skin color and cultural expression tied to basic views of ethnic backgrounds, the use of race becomes a choice that says something about the person choosing to do so. If we choose instead to view human beings as genetically the same with variations in abilities being a mix of genes and environment, one has to take a much more culturally introspective position. If there are legitimate differences on performance, there have to be reasons tied to cultural and evolutionary pressures that can't cross the line into legitimate defined boundaries between subspecies of Homo sapiens. Are we choosing to say there are subspecies or varieties of Homo sapiens?

I'm sure Murray has his own opinions on this, but in The Bell Curve at least, he doesn't dare offer his speculations. In his analysis, somebody is "black" if they self-identify as such, and being "black" means nothing more nor less than this self-identification. He then compares IQ test scores across populations, controlling for every possible socioeconomic variable that he can, and finds out that even when controlling for how much schooling you've had, what schools you go to, whether your parents are married, what your household income is, whether your parents graduated from college, etc., whether or not you self-identify as "black" still has predictive power.

The way he sets this up, he provides a ton of ammo to people who think that race is a well-defined biological thing and that some races are morally and intellectually superior to others. But he doesn't go all the way out and state anything.

In fact, he repeatedly and adamantly says that everyone should be treated as individuals regardless of race, and if somebody has an IQ of 135, he can be expected and should be equally encouraged to do everything that such bright people do, regardless of race. The message is that although different people have different potentials, everybody should be encouraged to reach their maximum potential. So in that sense, the actual message is that we shouldn't worry about "race", whatever that might be. But the price of not worrying about race is that we likewise shouldn't freak out if one race or another happens to be underrepresented (or overrepresented) on the campuses of elite law schools and such.

[_EAllusion]

I think you are conflating IQ and what IQ is purporting to measure in your response Analytics. You don't take Calculus to improve your general intelligence (at least for argument's sake, because that's disputable), but mastering Calculus is going to be highly beneficial to your ability to perform well on high school math problems you find in tests like the SAT. Since we are deriving statements about IQ from those tests' inter-test reliability with IQ measures, the implication is that varience in IQ will depend on whether varience in mathematics education affects how well you do in math up to and including calculus. Regardless of how you come down on that question, it has implications I don't think you have accepted.

You seem to be just assuming that more effectively learning Calculus doesn't change your IQ, when that very point is in dispute. The SAT math questions are high school math problems generally in story form. If better schooling can make you better at that, it will necessarily reflect in SAT scores. The single biggest skill for that kind of problem is understanding the underlying math.

If is very difficult to imagine a world I which learning to be good at Calculus doesn't help you also be good at the SAT.

[_Some Schmo]

On top of that, you'll hear him say things on his podcast with confidence that are wrong or only one of a number of potential positions, things like that, and if it comes up in the discussion it gets turned into a battle to the intellectual death.

Just so we're clear, I don't necessarily fault to anyone for reacting emotionally to Harris. There are certainly public figures that annoy me too. I do object to people making accusations about him that are patently false, however, as a result of that emotion.

As I consider your comments (and I do take them seriously enough to consider them as honestly as I can) I begin to wonder how much Harris's personality might be sitting in one of my own blind spots. The thing is, I find myself listening to him these days looking for problems with the way he's arguing and not finding them. Is it because I'm not seeing the complete picture on any given topic (of course, that must be part of it) or is it just that I find myself generally agreeing with his point of view?

This last conversation I listened to with Ezra Klein, for instance, I wanted to give Klein a fair shake, since I realized early in the conversation I was aware of him from other articles I'd read that I liked (I hadn't read the email exchange between them because I didn't know all the back story and frankly didn't care). Throughout the entire conversation, it seemed to me that Klein was actively ignoring the point of what Harris was saying. I thought Harris addressed Klein's primary complaint early and up front, and it seemed to make no impact on him at all.

Is this me cheerleading for Harris or just interpreting the conversation as I heard it? I'm wary of being a Harris booster, but when I hear something and react to it as honestly as I can, I'm not sure that's succumbing to bias rather than just calling the conversation as I see it. It's probably both.

So anyway, I'm only mentioning all this because I'm aware of the possibility that I'm missing something, but it certainly feels like a lot of people's complaints about him are rooted more in emotion than logic. It appears to me that some people just don't like his style, and they conflate that with the veracity of his comments.

[_Analytics]

I think you are conflating IQ and what IQ is purporting to measure in your response Analytics. You don't take Calculus to improve your general intelligence (at least for argument's sake, because that's disputable), but mastering Calculus is going to be highly beneficial to your ability to perform well on high school math problems you find in tests like the SAT. Since we are deriving statements about IQ from those tests' inter-test reliability with IQ measures, the implication is that varience in IQ will depend on whether varience in mathematics education affects how well you do in math up to and including calculus. Regardless of how you come down on that question, it has implications I don't think you have accepted.

You seem to be just assuming that more effectively learning Calculus doesn't change your IQ, when that vary point is in dispute. The SAT math questions are high school math problems generally in story form. If better schooling can make you better at that, it will necessarily reflect in SAT scores. The single biggest skill for that kind of problem is understanding the underlying math.

I precisely understand the difference between g, IQ tests, and the SAT. All I'm saying is that scores on the SAT correlate very highly with scores on standardized tests of intelligence, and like IQ scores, are stable across time and not easily increased through training, coaching or practice. SAT preparation courses appear to work, but the gains are small — on average, no more than about 20 points per section. The only reason I believe this is because experts who make a career out of studying these things come to that precise conclusion based on data.

You seem to take issue with this conclusion because it doesn't conform to your own preconceptions about the SAT and your logical analysis of it. The situation reminds me of the motto of the Society of Actuaries, "The work of science is to substitute facts for appearances, and demonstrations for impressions. -Ruskin"

[_EAllusion]

You are confusing the results of college preparation courses on those who opt to take them with quality of schooling from basic numeracy to advanced calc. This leads to exotic claims like Jamie Escalante's students might be good at calc, but that won't translate into SAT math performance. Of course it will and the contrary claims miss the point. What got this tangent started was me pointing out a distiction between cramming and having a solid educational base fostered over years.

P.S. There is more variation the research on the effects of college preparation courses on SAT scores that the number you are citing. It's just not relevant to the point being discussed.

E.g. https://www.washingtonpost.com/news/ans ... -says-yes/

[_Analytics]

You are confusing the results of college preparation courses on those who opt to take them with quality of schooling from basic numeracy to advanced calc. This leads to exotic claims like Jamie Escalante's students might be good at calc, but that won't translate into SAT math performance. Of course it will and the contrary claims miss the point. What got this tangent started was me pointing out a distiction between cramming and having a solid educational base fostered over years.

Fundamentally I am an empiricist, EA. If Jame Escalante's students (or any other group of students) in a controlled experiment had their SAT scores significantly increase by taking Calculus, that would prove that you are right and that David Hambrick is wrong. Until then, I'm going to believe that "Scores on the SAT correlate very highly with scores on standardized tests of intelligence, and like IQ scores, are stable across time and not easily increased."

That said, I am fan of the Khan Academy and I'm not that surprised that their course does a better job of increasing SAT scores. If the Khan Academy can also help people increase their IQs, that is great news.

[_EAllusion]

You are confusing the results of college preparation courses on those who opt to take them with quality of schooling from basic numeracy to advanced calc. This leads to exotic claims like Jamie Escalante's students might be good at calc, but that won't translate into SAT math performance. Of course it will and the contrary claims miss the point. What got this tangent started was me pointing out a distiction between cramming and having a solid educational base fostered over years.

Fundamentally I am an empiricist, EAllusion. If Jame Escalante's students (or any other group of students) in a controlled experiment had their SAT scores significantly increase by taking Calculus, that would prove that you are right and that David Hambrick is wrong. Until then, I'm going to believe that "Scores on the SAT correlate very highly with scores on standardized tests of intelligence, and like IQ scores, are stable across time and not easily increased."

Again, there is a significant difference between 2-20 hours of college entrance exam preparation and the sum-total effects of quality of math education starting at the post-elementary level on math performance. It is not helpful to equate the two. One of the things that tends to be stable across time is a person's educational experience as people largely stay within educational tracks, especially as it relates to learned skills building upon themselves. What we are interested in is whether varying quality of schooling has an impact. If it doesn't, then let's get to cutting. If it does, then the story of relatively immutable IQ as measured by proxy converting aptitude tests for the military doesn't hold up well. Either way, pick a horn of the bull.

Your response to this is to suppose that quality of education can impact how well you understand subjects like Algebra and calculus and perform on tests testing that knowledge (thereby justifying paying for better education), but that doesn't meaningfully correspond to how well you will do on math tests found on tests like the ASVAB and SAT. This is a rather dubious claim that isn't backed up by what you are citing. Arguing that a relatively brief crash-course doesn't move numbers much cannot function as an equivalent variable to quality of schooling. Further, wrapping yourself up in the authority of David Hambrick just is off point for what you are claiming. If you want to cite someone directly arguing that significantly improving achievement through schooling in high level math like what is found in an AP calc exam, or even the ACT, doesn't also improve SAT math scores, go for it. Mind you, the correspondence between ACT math and SAT math performance is quite high and differences between the two can be in part explained by the fact that the SAT's story-problem style also tests reading comprehension more.

[_Analytics]

Fundamentally I am an empiricist, EAllusion. If Jame Escalante's students (or any other group of students) in a controlled experiment had their SAT scores significantly increase by taking Calculus, that would prove that you are right and that David Hambrick is wrong. Until then, I'm going to believe that "Scores on the SAT correlate very highly with scores on standardized tests of intelligence, and like IQ scores, are stable across time and not easily increased."

Again, there is a significant difference between 2-20 hours of college entrance exam preparation and the sum-total effects of quality of math education starting at the post-elementary level on math performance. It is not helpful to equate the two. One of the things that tends to be stable across time is a person's educational experience as people largely stay within educational tracks, especially as it relates to learned skills building upon themselves. What we are interested in is whether varying quality of schooling has an impact. If it doesn't, then let's get to cutting. If it does, then the story of relatively immutable IQ as measured by proxy converting aptitude tests for the military doesn't hold up well. Either way, pick a horn of the bull.

Your response to this is to suppose that quality of education can impact how well you understand subjects like Algebra and calculus and perform on tests testing that knowledge (thereby justifying paying for better education), but that doesn't meaningfully correspond to how well you will do on math tests found on tests like the ASVAB and SAT. This is a rather dubious claim that isn't backed up by what you are citing. Arguing that a relatively brief crash-course doesn't move numbers much cannot function as an equivalent variable to quality of schooling. Further, wrapping yourself up in the authority of David Hambrick just is off point for what you are claiming. If you want to cite someone directly arguing that significantly improving achievement through schooling in high level math like what is found in an AP calc exam, or even the ACT, doesn't also improve SAT math scores, go for it. Mind you, the correspondence between ACT math and SAT math performance is quite high and differences between the two can be in part explained by the fact that the SAT's story-problem style also tests reading comprehension more.

If you don't think SAT scores are stable across time and do think they are easily changed, I encourage you to write a formal paper and submit it to a journal. Stop arguing with me about it.

Obviously, we aren't communicating here. Murray says that a child being raised in a good adopted home as opposed to a bad home is proven to increase his or her IQ. As far as I can tell, the research he cites does in fact prove this. But you seem to insist that he (and by extension me) doesn't really believe this. Thus you argue with what you think he believes rather than with what he says.

Perhaps the fundamental problem here is that I believe the research indicates what Murray claims it does, while in contrast, you use your mindreading abilities to determine when Murray is sincere and isn't, and then somehow believe that what I'm saying is consistent with your caricature rather that with the research.

Your posts of the form "you believe x which implies y which implies z which makes no sense" simply prove that you don't understand my position--not that I'm wrong.

[_EAllusion]

If you don't think SAT scores are stable across time and do think they are easily changed, I encourage you to write a formal paper and submit it to a journal. Stop arguing with me about it.

Here you are attempting to pit yourself on the side of what research says and imply I'm challenging it, when in reality you're just not getting the point. If you pluck and 8 year old, give them a battery of mental tests, then find that same 8 year old when they are 17 and have them take an SAT, you can get good reliability between tests. This actually has little to do with what is being disputed here, which is a unique byproduct of you not being willing to accept the implications of what you think is the case and resolving it by adopting a dubious position you've cited no evidence in favor of.

Murray does not think what you think on this point. He believes that, and has written quite a bit about, the idea that it is relatively futile to teach low IQ students high end material. You're the one proposing a clean decoupling of high-end math achievement with ability to answer SAT math questions.

Obviously, we aren't communicating here. Murray says that a child being raised in a good adopted home as opposed to a bad home is proven to increase his or her IQ.

It's important to note here what Murray actually says is that this has to be done very early on because IQ is relatively immutable regardless of social circumstance from early childhood on. You can't adopt a 12 year old and get this effect, per Murray.

Perhaps the fundamental problem here is that I believe the research indicates what Murray claims it does, while in contrast, you use your mindreading abilities to determine when Murray is sincere and isn't, and then somehow believe that what I'm saying is consistent with your caricature rather that with the research.

Murray's claims range from reasonable, but subject to some dispute to quite controversial to unethical pseudoscience bad enough to deserve censure. It doesn't help that he is selective and sloppy even when on the reasonable side of the fence, so it's hard to respond to this assessment. I'm not proposing mind-reading Murray, though. When I say he implies something, what I mean is that it is the natural point of his statement, not that we have to mind-read him. When he points out that black African IQ is near borderline, but South African black IQ is higher and near identical to African Americans, then takes specific note that they share similar white admixture, he's telling you he thinks that genetics explains this phenomenon. It's implied, but we don't need to mind-read to get his point. When he writes, quite extensively, about how programs that provide material assistance to the poor encourage the low IQ people to breed and increase social ruin, he's telling you that those programs are bad for that reason. He's making a pro-eugenic argument. We don't need to mind-read him on that point. We just need to have basic inference skills.

Your posts of the form "you believe x which implies y which implies z which makes no sense" simply prove that you don't understand my position--not that I'm wrong.

I'm criticizing you for not accepting the consequence of what you say you believe. It's probably because your ideological views are coming into conflict with your desire to to champion The Bell Curve.