The Bell Curve

[_beastie]

I might be confusing the two concepts a little, but I'm thinking specifically of "The Iowa Tests" which we took in Utah back then. I suppose those are geared towards academic achievement, but there must be an intelligence component. When I was in the second grade and the teacher was trying to justify putting me in resource, it must have been a more general intelligence test, right? Reflecting upon it, I've always had a really good ability to focus on something that really captures my attention, but I've always found it incredibly difficult to focus on what other people tell me to or on something that just isn't turning my brain on. When little I was notorious for intensely daydreaming. Looking back at it, maybe I really was smart (my mom always thought I was, lol), but when I sat down to take tests I spaced out and looked like I should be placed in resource. As I got older I slowly learned how to concentrate, somewhat. A friend who is a doctor heard about these struggles and said he thought I might have ADD. I saw a psychologist about it, took a test, and was diagnosed with it.

My middle school had this single math placement test they gave every student at the beginning and end of every year. Some of the questions depended on whether you'd been exposed to specific math concepts of course, but some of it clearly tested for g. I still remember one of the questions I got right that stumped most of the seventh graders in the "smart" class. The question was "150% of 12 =". Nobody knew how to approach that. Explaining the solution, Mr. Carrier said, "'of' means multiply and 150% means 1.5. So you multiply 1.5 by 12." We didn't have calculators of course and 1.5 wasn't on the multiplication table, so he calculated that out the long way. Everybody stared at the board collectively thinking WTF. I didn't get what he was doing either. One of the smart popular kids looked over at my sheet and saw that I got it right. He asked me how I did it. I said, "Well, 100% of 12 is 12 at 50% of 12 is 6, and 12 + 6 is 18." The kid yelled out, "Mr. Carrier! I like Analytic's solution better!"

I totally hear you on the observer-expectancy thing. I went to a fairly large middle school, and after being in the top of the advanced class for two years, I walked into Geometry on the first day of the 9th grade and sat down. One of the "smart" kids saw me and was sure I was in the wrong place. "This is GEOMETRY Analytics! This class is for the SMART kids. NOT YOU! Let me see your schedule printout and I'll tell you what class you should head to."

The Iowa Test of Basic Skills was a very widely test administered a couple of decades ago. It is an achievement test, not an IQ test. Someone with ADD would be severely disadvantaged on the test (as, indeed, they are on most tests) because it is strictly timed. I do not remember any IQ component at all. Whether or not a teacher would recommend you for special placement based solely on that test depends on the individual school and district. My school did, indeed, use that test for years to determine placement in remedial reading classes, decades ago.

The only "sort of" IQ tests regularly administered to elementary students is called the Otis Lennon. In my state, it's administered in the second and fourth grades. It's only "sort of" an IQ test because it is a group administered test, which means it's unreliable. Mainly teachers use it to spot wide discrepancies between verbal and nonverbal scores, which can be an indicator of a learning disability, but I doubt any school would use it as a serious reference point during an eligibility hearing.

It is difficult to obtain a reliable IQ score on young children, anyway.

I also read the book when it came out, and agree with EA. But either I threw away my copy or got it from the library, because it is no longer in my personal library.

in my opinion, it's almost impossible to avoid bias in standardized testing.

[_Always Changing]

Mainly teachers use it to spot wide discrepancies between verbal and nonverbal scores, which can be an indicator of a learning disability, but I doubt any school would use it as a serious reference point during an eligibility hearing.

no, not allowed. Must be individually administered, because of the vagaries of motivation and attention and concentration. You can pick up on those when doing the testing, if you are competent and concerned about ethical issues. Now, if you are interested in using special education to resegregate, you can also tweak things.

[_EAllusion]

Again, "Bell Curve" was written to justify cutting off funds for leveling the playing fields between social classes.

I don't think there's any question about that when you look at Murray's political advocacy both before and after the book based on the same general arguments, the anti-policy that makes up the book's recommendations, the other policies they hint towards, but do not state, and the some of the key resources behind the book.

I don't want to focus on that because I don't want that to be viewed as poisoning the well, but if someone wants to challenge whether the book is an attempt to underwrite a sort of social Darwinism with racial overtones via eliminating redistribution programs meant to provide opportunity to the disadvantaged, then I think that's the place you have to go. The broad sweep of the book is quite libertarian in its policy aims, which I share in plenty of cases for completely different reasons, but that's where it goes. Murray would tell you that the policy implications are secondary to this abstract stratification story they are telling, but then again, Murray has made a career out of providing a case for such policy based on the stories he's telling.

Murray's schtick is to say something like that job training programs for people receiving public assistance are probably going to be highly ineffective because people on public assistence are, on average, pretty dumb and it's really hard to fix dumb with training. Take that information what you will. He doesn't want to see anyone get hurt or anything. He's not saying throw the poor to the wolves. Also, it's shame if the poor live lives so comfortable because of assistance that we accidentally encourage them have children who will inherit their dumb genes. Do we want that social burden? He's not a eugenicist here. He's just sayin'.

Analytics seems itchin' for that fight, but maybe not? I'm not sure? Why bring up if a single paragraph is sufficiently Fox News friendly?

[_Analytics]

I might be confusing the two concepts a little, but I'm thinking specifically of "The Iowa Tests" which we took in Utah back then. I suppose those are geared towards academic achievement, but there must be an intelligence component. When I was in the second grade and the teacher was trying to justify putting me in resource, it must have been a more general intelligence test, right? Reflecting upon it, I've always had a really good ability to focus on something that really captures my attention, but I've always found it incredibly difficult to focus on what other people tell me to or on something that just isn't turning my brain on. When little I was notorious for intensely daydreaming. Looking back at it, maybe I really was smart (my mom always thought I was, lol), but when I sat down to take tests I spaced out and looked like I should be placed in resource. As I got older I slowly learned how to concentrate, somewhat. A friend who is a doctor heard about these struggles and said he thought I might have ADD. I saw a psychologist about it, took a test, and was diagnosed with it.

My middle school had this single math placement test they gave every student at the beginning and end of every year. Some of the questions depended on whether you'd been exposed to specific math concepts of course, but some of it clearly tested for g. I still remember one of the questions I got right that stumped most of the seventh graders in the "smart" class. The question was "150% of 12 =". Nobody knew how to approach that. Explaining the solution, Mr. Carrier said, "'of' means multiply and 150% means 1.5. So you multiply 1.5 by 12." We didn't have calculators of course and 1.5 wasn't on the multiplication table, so he calculated that out the long way. Everybody stared at the board collectively thinking WTF. I didn't get what he was doing either. One of the smart popular kids looked over at my sheet and saw that I got it right. He asked me how I did it. I said, "Well, 100% of 12 is 12 at 50% of 12 is 6, and 12 + 6 is 18." The kid yelled out, "Mr. Carrier! I like Analytic's solution better!"

I totally hear you on the observer-expectancy thing. I went to a fairly large middle school, and after being in the top of the advanced class for two years, I walked into Geometry on the first day of the 9th grade and sat down. One of the "smart" kids saw me and was sure I was in the wrong place. "This is GEOMETRY Analytics! This class is for the SMART kids. NOT YOU! Let me see your schedule printout and I'll tell you what class you should head to."

The Iowa Test of Basic Skills was a very widely test administered a couple of decades ago. It is an achievement test, not an IQ test. Someone with ADD would be severely disadvantaged on the test (as, indeed, they are on most tests) because it is strictly timed. I do not remember any IQ component at all. Whether or not a teacher would recommend you for special placement based solely on that test depends on the individual school and district. My school did, indeed, use that test for years to determine placement in remedial reading classes, decades ago.

The only "sort of" IQ tests regularly administered to elementary students is called the Otis Lennon. In my state, it's administered in the second and fourth grades. It's only "sort of" an IQ test because it is a group administered test, which means it's unreliable. Mainly teachers use it to spot wide discrepancies between verbal and nonverbal scores, which can be an indicator of a learning disability, but I doubt any school would use it as a serious reference point during an eligibility hearing.

It is difficult to obtain a reliable IQ score on young children, anyway.

I also read the book when it came out, and agree with EA. But either I threw away my copy or got it from the library, because it is no longer in my personal library.

in my opinion, it's almost impossible to avoid bias in standardized testing.

Great information Beastie. And it's great to hear from you--thanks for weighing in.

[_Always Changing]

The basic gist is that having a high IQ has a very economic value that is increasing. While we aren't there yet, we are moving in the direction of a meritocracy where everybody who has a high IQ, regardless of their race, religion, sex, or background, will find there way to congregate in schools, jobs, and neighborhoods with other people with high IQs.

Yeah, right. Intense sarcasm. And those at the top of the economic ladder will think that the hoi polloi are all a bit, you know, retarded. When, unknown to them, there are some brilliantly creative iconoclasts who are planning on doing what they do best.

[_Always Changing]

The broad sweep of the book is quite libertarian in its policy aims, which I share in plenty of cases for completely different reasons, but that's where it goes. Murray would tell you that the policy implications are secondary to this abstract stratification story they are telling, but then again, Murray has made a career out of providing a case for such policy based on the stories he's telling.

Analytics seems itchin' for that fight, but maybe not? I'm not sure? Why bring up if a single paragraph is sufficiently Fox News friendly?

My previous post covers that. The issue isn't done until the school systems identify every gifted child cowering before a teacher who thinks the child has no right to be gifted, based on all the negative expectations.

This is a RECENT reprise on an old study. http://mediasurvivor.com/categories/dat ... roves.html Nothing has changed.

[_Analytics]

Circling back to the Thomas Sowell review for a second, one of the things the authors of the Bell Curve are going to argue is that cultural biases on IQ measures are a red herring / not relevant, because the submeasures that you'd expect to be the least culturally dependent, and the ones that correlate best with g in factor analysis, are the ones that the poor performing ethnic groups do the worst one. In other words, while performance on vocab dependent tests that by necessity are going to have some bias related to one's language experiences are worse, more abstract measures like spatial reasoning are even worse than that. This isn't what you'd expect if the problem was just cultural biases built into the tests.

Their stronger argument, IMHO, is the predictability aspect. Assume the SAT was significantly biased against blacks and thus isn't a fair and accurate predictor of how well they'll do in college. If that were true, then you'd be able to see the results by how well they do in college. It turns out, according to what we both heard in that damned Harris podcast that started this discussion, that blacks with an SAT score of 480 do just as well in college as whites that get an SAT score of 480.

The counterargument would probably be that the college curriculum is biased against blacks in the same way that the SAT score is. Thus a black with a SAT score of 480 actually has a g than a white with an SAT of 480, but it doesn't translate into college performance because of the cultural bias in school.

But that doesn't negate the actual point. The actual point is that intelligence, as measured by standardized tests, is an excellent predictor of subsequent performance.

[_Analytics]

Murray's schtick is to say something like that job training programs for people receiving public assistance are probably going to be highly ineffective because people on public assistence are, on average, pretty dumb and it's really hard to fix dumb with training. Take that information what you will. He doesn't want to see anyone get hurt or anything. He's not saying throw the poor to the wolves. Also, it's shame if the poor live lives so comfortable because of assistance that we accidentally encourage them have children who will inherit their dumb genes. Do we want that social burden? He's not a eugenicist here. He's just sayin'.

Analytics seems itchin' for that fight, but maybe not? I'm not sure? Why bring up if a single paragraph is sufficiently Fox News friendly?

Am I itching for that fight? Hell no. As far as I can tell, I share your political sensibilities exactly. I'm all in favor of doing anything and everything that can be done to eliminate the disadvantages that black Americans face.

All I'm trying to do here is understand the actual arguments in the book, as stated.

[_Always Changing]

But that doesn't negate the actual point. The actual point is that intelligence, as measured by standardized tests, is an excellent predictor of subsequent performance.

Of course. But the individual who has not had the opportunities to achieve up to his/her potential (barring self-destructive activities brought about by a lack of hope) also often has enough of a hungry mind to search out informal learning situations (internet, library, etc), and enter higher education later.


Yeah, the book is a bit hypnotic. Like the Book of Mormon, maybe?

[Guest]

So if it is only a "modest correlation" defining this relationship, why is the entire book, so far, predicated on fully accepting this relationship and its predictive power, including averages, for specific groups of people?

Great question. The way these models work is that you have a big list of people in a population. You want to see if you can predict something for each person in the data (e.g. Y = income) by other elements of data (e.g. X1 = IQ, X2 = education level, X3 = race, X4 = income of parents, X5 = ZIP code, etc.). You do some fancy math and make an analysis about various pitfalls and see if there is a relationship. The relationship is going to be of the form:

Y = B1*X1 + B2*X2 + B3*X3 + B4*X4 + e

In this example, X1, X2, X3, and X4 are four specific factors that vary by individual, and Y is each individual's income. If the relationship is actually there and the formula is set up correctly, you can calculate what B1, B2, B3, and B4 are--those are the factors that make the prediction. By the math, you can calculate what they are and see if they actually have the ability to help predict Y if you know what B1, B2, B3, etc. actually are.

The final term is "e". This is the residual. The idea is that when you do the study, X1, X2, etc. can help predict Y, but they will rarely predict it exactly. "e" is the missing piece--the part that isn't explained by the model. If the model is good, then "e" will be normally distrusted around zero and independent from person to person.

What the book is saying that out of all of the factors we have in our data, IQ does the very best job of predicting success. It doesn't predict it perfectly--some people with low IQs make good, and others with very high IQs are colossal failures. Everybody does at least a little better or a little worse than what the model predicts. Despite that, there is a clear, mathematical relationship and that out of everything that is modeled, IQ is the most powerful indicator of success.

So how should this be applied? When this is applied to the population as a whole, it gives very powerful results. Have you seen the movie Money Ball? It is kind of like that. On any given baseball play anything could happen. But over the course of a season, patterns emerge. If you understand those patterns, powerful things can happen.

Does that help?

Thank you so much. I'm sure my students will appreciate reading your analysis as some sort of case study in applied statistics when they take my economic policy analysis course.

You are apparently addressing ONLY my last sentence, and that out of context, as you apparently thought I was asking you how regression analysis "works." I was not. I was actually pointing out that when you said the authors defined "a modest correlation" on one variable, combined with, as you also said, "individual factors that don't come through in the statistics [which] are collectively the driving determinants of success," you were not defining a regression that is reliably capturing the relationship, but more likely describing an issue with missing variable(s). You can't have it both ways.

Here is my actual comment addressing this, prior to that last sentence you quoted:

So if individual factors, NOT captured by the statistics, are the "driving determinants" of success, then the only way that IQ could still have "the most predictive power" would be if those individual factors WERE correlated with IQ. But the main argument of these outliers, if I am reading you correctly, was that these individual factors were NOT correlated with IQ. So, which is it? IQ predicts? Or individual factors predict? Or is it that the authors are carefully asserting no individual is being talked about here, but their analysis still holds for groups and averages, hence EA's "exaggerated relationship" comment?