Scientists Meredith C. Frey and Douglas K. Detterman came up with a formula for predicting how one would score on an official IQ test from their performance on the post-1995 SAT. The formula was presumably derived from regression predicting IQs on the Raven Advanced Progressive Matrices (RAPM) from scores on the SAT (see scatter-plot C below) of 104 students at a selective private university.

Such formulas are useful, because if you ever hit your head, a psychologist might administer an IQ test to see if you have brain damage. But if you score low, it doesn’t necessarily prove any damage; it could just be that you’re naturally dumb. Thus knowing your statistically expected performance on an official IQ test from your past performance on tests like the SAT is diagnostically useful.

The formula is as follows:

X’IQ = (0.095 * SAT-M) + (-0.003 * SAT-V) + 50.241

It is interesting to apply this formula to the average Harvard student who scored 1490 on the SAT (reading + math). Assuming the typical Harvard undergrad scored 745 on both the reading and the math section, the formula predicts they will score 123 on an official IQ test. Note, 123 is NOT their SAT score converted to an IQ equivalent, it’s their expected IQ on a different test, given their score on the SAT, and thus there is severe regression to the mean.

A predicted IQ of 123 remarkably similar to the mean IQ of 122 a sample of Harvard students actually obtained when tested on the WAIS. Some readers might be wondering why I’m not equating the predicted IQ to white norms as I normally do. The answer is that the RAPM was normed in Iowa (one of the 5 whitest states in America) so converting to white norms would be redundant.

One possibility is that this formula underestimates the expected intelligence of high SAT people because the scatterplot clearly shows a pile up of scores at the ceiling of the RAPM, however this pileup only seems to consist of 12% of the sample (not enough to significantly flatten the regression line, especially since some of them would have scored the same even if the test had more hard items).

In addition, I personally looked at the scatter plot carefully and did my best to write down the RAPM IQs of every single participant with an SAT score from 1400-1600. This was an admittedly subjective and imprecise exercise given how small the graph is, but I counted 38 top SAT performers and these were their approximate RAPM IQs: 95, 102, 105, 108, 108, 110, 110, 113, 113, 113, 113, 113, 117, 117, 117, 117, 117, 120, 120, 120, 122, 122, 128, 128, 128, 128, 134, 134, 134, 134, 134, 134, 134, 134, 134, 134, 134, 134.

While the mean RAPM IQ of the top SAT performers was likely reduced by ceiling bumping, the median wold not have been, and that median was 120, suggesting the regression line prediction of 123 was not too low.

An RAAPM IQ of 123 is 26 points above the U.S. mean IQ of 97. An SAT score of 1490 equates to an IQ of 139…or perhaps 137 if a many SAT takers are tested repeatedly and use their best score as commenter Lion of the Judah-sphere suggested… about 40 points above the U.S. mean of 97. Dividing 26 by 40 suggests the SAT and RAPM correlate 0.65. If we assume that the correlation between the SAT and Raven is entirely caused by g (general intelligence)…a reasonable assumption given they have little in common but reasoning.. and if we further assume that the RAPM has a g loading of 0.85, then we can deduce that the SAT has a g loading of 0.76 (0.65/0.85).

A respected blogger named Emil has responded to my recent post about Harvard students regressing precipitously to the mean when they take an official IQ test. Although some studies have found the SAT only correlates 0.4 with official IQ tests like the WAIS, Emil writes:

The lower values are due to restriction of range, e.g. Frey and Detterman (2004). When corrected, the value goes up to .7-.8 range. Also .54 using ICAR60 (Condon and Revelle, 2014) without correction for reliability or restriction.

While it’s certainly true that the SAT’s correlation with official IQ tests goes way up when you correct for range restriction, I’m not sure how appropriate the correction is here. The point of such corrections is that if a sample has a restricted range of general intelligence (g), but an unrestricted range of non-g variance, then almost by definition, variance in g will have less predictive power than non-g variance, since the latter variance exceeds the former.

However people who take the SAT, particularly at the same high school, are not just restricted in g, but are also restricted in academic background and test preparation which likely correlates with SAT scores independently of g, thus studies that correct for range restriction in g, while ignoring range restriction in non-g variance, may grossly overestimate the SAT’s correlation with IQ in a random sample of all American 17-year olds.

Emil also notes the average IQs of Harvard students in the study I cited might be deflated by an oversampling of social science students who are less intelligent than STEM students. I definitely agree that STEM students are more intelligent than social science students, however I’m not sure this would have a significant effect because most Harvard students are not in STEM, so the non-STEM students would probably be a lot more representative of the average Harvard undergrad than STEM students are. However this needs to be explored in more depth.

Emil then writes:

SAT has an approx. mean of ~500 per subtest, ceiling of 800 and SD of approx. 100. So a 1500 total score is 750+750=(500+250)+(500+250)=(500+2.5sd)+(500+2.5sd), or about 2.5 SD above the mean.

I realize Emil is just doing a rough estimate, but it’s important to note that verbal and math sections of the SAT are said to only correlate about 0.67, so someone who scored +2.5 SD on each subscale should be about +2.8 SD on the composite (relative to the SAT population, who are already above the U.S. population mean). At least in theory..

Official stats from the year 2000 (around when the Harvard students in the cited study were tested) showed that the national mean verbal SAT was 505 (SD = 111) and the mean math SAT was 514 (SD = 113) and the composite score had a mean of 1019 (SD = 208). Assuming Harvard students have a mean SAT of 1490, they would have scored 2.26 SD higher than the average SAT taker. Roughly the top one in 85 SAT takers, and probably the top one in 255 level for all American 17 year olds (+2.66 SD).

Emil then applies the 0.86 test-retest correlation to estimate how SAT takers will score on the WAIS, however this correlation might be way too high because it is based on people taking the same test twice and the SAT and WAIS are not the same test. One’s true score on the SAT will not correlate perfectly with one’s true score on the WAIS.

People who score +2.26 SD above the SAT population on the SAT will average 0.86(2.26 SD)= 1.94 SD when they take the SAT again, which is the top 2.6% with respect to SAT takers, and the top 0.88% of all 17 year olds, equivalent to an IQ of 136 (U.S. norms) or IQ 134 (U.S. white norms) or IQ 132 (U.S. normal white norms). By contrast on the WAIS Harvard students average IQ 122 (U.S. normal white norms; corrected for test abbreviation).

In short, the unreliability of the SAT does not seem to explain the severe regression to the mean Harvard students experience when tested on the WAIS.

I recently saw the new movie Gone Girl staring Ben Affleck and Rosamund Pike (spoiler alert). One of the characters is a Harvard grad who creates a fake identity as a working class person. While hanging out with working class friends, she accidentally drops a huge stash of cash on the ground, exposing the fact that she is much richer than she has been pretending to be. A little later, the two working class friends (a man and woman) show up at the Harvard grad’s apartment. They force their way in and start turning over furniture until they find all her cash and leave with it. The Harvard grad threatens to call the police, but one of the “friends” say something like “Lady, you’re hiding. I don’t what from, and I don’t care, but you ain’t calling no police.”

It was an interesting scene, because the Harvard grad had been placed at the top of society, artificially, by high SAT scores and the Ivy League caste system, but by making a dumb mistake in the real world (failing to hide her money) she was dominated by the Darwinian law of the jungle (might is right). In the end, nature always wins.

In reminded me of an episode of The Sopranos where Carmela (the wife of mobster Tony Soprano) wants to get their daughter into an elite school. She turns to a neighbor (who has a sister who works as a professor at the elite college) to ask if her sister can pull some strings. The neighbor dodges the question by saying something like “with your daughters great grades and SAT score, she doesn’t need my sister’s help getting in.” But Carmela explains that these days, elite colleges are so competitive that high grades and high test scores are not enough.

So reluctantly, the neighbor phones her professor sister to try to get her to write a letter of recommendation for Carmela’s daughter. Absolutely not, responds the professor, explaining that it’s a prestigious college so they can’t have the children of gangsters crawling around the campus. When the neighbor explains to Carmela that her sister can’t write the letter, Carmela is nonplussed.

Carmela decides to visit the professor at her office, bringing lazania as a gift. She introduces herself and asks if the professor can write the letter. The professor makes up some excuse about having to write a letter for some other worthy student. Carmela says the solution is simple, just explain to that student that you can’t write the letter for him. The professor explains that she can’t.

“I don’t think you understand,” says Carmela ominously. “I want you to write that letter”

“Are you threatening me?” asks the professor trembling.

“Who’s threatening? I brought you some lazania,” Carmela replies.

Being smart enough to take the hint and realize you don’t fuck with a mobster’s wife, the terrified professor panics and writes the letter as fast as she can and Carmela’s daughter is accepted into the school post haste. It was interesting, because you think of Tony Soprano as being the tough one in the family, but you can see that his wife has a little of the mobster toughness in her too, but is more subtle about it, and uses it to advance more feminine goals (getting their kid into a good college).

It’s interesting that the despite needing a letter of recommendation, the Soprano daughter was academically qualified to attend the elite school. She probably inherited high IQ genes from Tony Soprona who in one episode stated that his IQ is 136. I remembered thinking this is quite high because although mobsters are rich (a sign of high IQ), they’re also violent criminals with typically low education (both signs of low IQ), so on balance, their IQs should be above average, but nothing special. John Gotti for example had an IQ of 110. But then Tony Soprano seems to have a huge cranium.

Even though it makes perfect sense that IQ and money would be positively correlated, the idea has encountered enormous resistance, even among some people who believe intelligence tests are excellent measures of innate intelligence. There are several reasons for this backlash:

1) Intelligence and income are two of the most highly valued traits, so suggesting a correlation between the two can be taken quite personally given the enormous income inequality in America. It’s bad enough that income helps determine our quality of life and social status, but to have it reflect our intellect too seems unfair and makes people very jealous.

2) As income inequality continues to grow, so too does resentment for the super-rich, especially in a bad economy. People would prefer to demonize rich people for being greedy and unethical than credit them for being smart.

3) Even people with limited education can get rich. This is very upsetting to people who are not rich despite attending the best schools or obtaining advanced degrees. They were told that the were superior to less educated people and are deeply invested in the Ivy League caste system, so to see some high school dropout who mispronounces words make a hundred times more money than they do, generates enormous rage. The rage can only be placated by telling themselves that the gazillionaire, despite his financial superiority, is intellectually inferior; genetically inferior. Thus the correlation between IQ and income must be denied, or at least dismissed as a statistical artifact with no direct causal implications.

4) Many of the most valuable people in history were not especially rich. Suggesting money reflects income is upsetting to the fans of such people. Although many of us understand that correlations are general trends that often don’t say much about specific individuals, when the subject is as sensitive as IQ and money, emotion trumps rationality, making it easier to just dismiss the correlation outright.

It’s interesting to observe the cognitive dissonance that occurs when you show people evidence that IQ in fact enjoys a robust positive correlation with income (+0.4).  Their first instinct is to say “well maybe low IQ predicts poverty, but there’s no evidence that high IQ causes above average income.”  This rationalization is win-win for the typical liberal, because it allows them to feel smarter than all the minimal wage Republicans working at Walmart without feeling dumber than the rich who they despise.

What happens when you cite evidence showing the IQ-income correlation is more or less linear through virtually the full range of IQs and virtually the full range of incomes?  Then the excuse becomes, correlation does not equal direct causation.  In other words, IQ causes education, and education causes income, but IQ does not cause income directly.  This excuse is a win-win for the Marxist Ivy League types because it allows them to feel smarter than less educated folks no matter how rich the latter are.  For they didn’t make the money the “correct” way; by going through the Ivy League gate keepers.

Such thinking helps to preserve the Ivy League caste system that elitists love because it stigmatizes the high incomes of non-Ivy League graduates as being a result of only luck, hard work, and sociopathic opportunism and denies the “free market” credit for rewarding talent.  Rather it is the Ivy League that rewards talent, and the “free market” only rewards talent to the extent it rewards Ivy League grads.  Thus anyone who gets rich or powerful without jumping through Ivy League hoops gets stigmatized as an enemy of meritocracy who must be destroyed.

Claiming that the IQ-income correlation is entirely mediated by education is also used by anti-HBD folks to deny IQ tests measure real world intelligence.   Instead, IQ tests are dismissed as only measuring narrow test taking skills that are useful for getting a degree, but it is the degree or the test scores that are rewarded by the “free market”, not the real world intelligent behavior of high IQ people. But what does the research show?  Scholar Ruth Berkowitz looked into the correlation between LSAT scores (a proxy for IQ) and income among lawyers.  She writes:

The regression results show that, across the top 50 schools, LSAT scores are significantly related to starting salary, even when controlling for the cost of living in the school’s location. One point on the LSAT is worth over $2,600 on the new scale…Of course, each point on the LSAT is not equal in terms of its effects on starting salary. At the high end of the scale, one point is worth much more than it is worth on the lower end of the scale. Without controlling for any other variables, a one point increase on the new scale on the LSAT (or a 1% increase at the mean) leads to a salary increase of $3,080 (8.5%) for the top 50 schools whereas a one point increase leads to only a $1,812 (6.2%) increase for all 177 schools combined… Similarly, moving up along percentiles on the LSAT distribution brings higher returns at the high end.

So among people with law degrees, LSAT scores and future incomes are substantially correlated.  But of course, not all law degrees are equal.  Do LSAT scores predict income among lawyers who attend the same law school?  The answer is yes:

The regression results for the individual data show that there is a significant (at the 5% level), albeit a smaller relationship between LSAT scores and starting salaries than there is for the cross-school model. Among the students in one school, one point on the LSAT is worth only about one-seventh of what it is worth in the cross-school model. These results indicate that six-sevenths of the variance is being used up in the screening effects of the school. Law schools have the ability to put more energy into screening students than do law firms. Law firms assume that in general, students attend the highest quality school into which they were admitted. Therefore, the true effect of one point on the LSAT is greater than can be measured within one school. However, in terms of lifetime income, the spread is still a significant difference even within one school. A student with a higher LSAT score, should, on average, make more money than a student who scored lower and attended the same law school. Between schools, the spread is larger. If a student scored in the top 5% on her LSAT and went to a top 5% school, she would be earning a higher salary, on average, than if she attended a lower ranking school.

So before controlling for what law school one attended, each point on the LSAT is worth $2,600, however among lawyers who attended the same law school, each LSAT point is worth only one seventh of that, so I assume $371 per year.  So, let’s say we have two lawyers who attended the exact same law school, John and Ted.  Let’s assume John got an LSAT score of 180 (equivalent to 152 on the IQ scale) and Ted got a score of 150 (equivalent to 111 on the IQ scale). This would predict an income difference of $11,130 dollars a year, or nearly half a million dollars over a 40 year career.  So in the typical case, there starting salaries would probably look something like this:

Same law school:

Ted LSAT IQ equivalent 111:  $70,000 starting salary, life time earnings over $2.8 million

John LSAT equivalent IQ 152: $81,130 staring salary, life time earnings over $3.2 million

Now a nearly half million difference is huge, but it might seem kind of small considering the two men differ by 41 IQ points.  However they only differ by 41 IQ points on the LSAT. Assuming the law school both men attended was average, if they were retested on the WAIS-IV, their IQs would regress to the mean IQ of lawyers nationally (IQ 125).  Because of a statistical phenomenon known as range restriction, among lawyers, especially lawyers at the same law school, the LSAT probably only correlates about 0.3 with scores on the WAIS-IV.  For example I found only a correlation of about 0.3 between self-reported LSAT scores and self-reported SAT scores, and others have a found a similar correlation between LSAT scores and Bar exam scores. A 0.3 correlation means that even though John was 41 IQ points smarter than Ted on the LSAT, he would likely be only 41(0.3) = 12 IQ points smarter than Ted on the WAIS-IV.

So the bottom line is that if you took the highest LSAT student and the lowest LSAT student at every law school, their WAIS-IV IQs would probably only differ by about a dozen points, and yet their life time earnings would differ by nearly half a million in today’s dollars. So even among people with identical schooling, even small differences in IQ are associated with huge differences in money:

Same law school:

Ted WAIS-IV IQ 121:  $70,000 starting salary, life time earnings over $2.8 million

John WAIS-IV IQ 133: $81,130 staring salary, life time earnings over $3.2 million

Of course it should be noted that while a 12 point IQ gap is associated with a half million difference among people who attended the same school, the same 12 point IQ gap would be associated with a $3.1 million life time earning difference when schooling is not controlled:

Different law schools:

Ted WAIS-IV IQ 121:  $70,000 starting salary, life time earnings over $2.8 million

John WAIS-IV IQ 133: $147,910 staring salary, life time earnings over $5.9 million

So while people like the Lion of the Blogosphere correctly assert that where you attend college is vastly more important to your income than how smart you are, being smart is still quite important in its own right.

Now in full disclosure, I should point out that another study found virtually no correlation between standardized test scores and income among graduates of the same business school.  Ronald Yeaple of authoritative Forbes magazine reports:

Our survey of hundreds of MBA alumni found no correlation between an individual’s GMAT score and that person’s post-MBA success as measured by starting salary and pay over the first five years after graduation. In this study of individual graduates, the R-square = 0.0007, which means that there was no correlation between GMAT scores and post-MBA earnings. Similar studies in the past gave the same result. Based on this research, the GMAT appears to have no power for predicting an individual prospective MBA student’s future career success. Some of the most successful managers in our study had below-average GMAT scores, and vice versa.

The explanation for this is probably that a lot of rich people use their influence to get their unqualified children into business schools they don’t qualify for, and then those same dumb trust fund babies are given a high paying job in the family business they’re also not qualified for, and delegate their responsibilities to higher IQ employees.  But in a field like law, where you actually have to interpret contracts and argue cases, it’s much harder for dumb rich kids to earn high incomes.

Commentator “Mugabe” mentioned a new blog post by scientist Steve Hsu asking whether Harvard discriminates against Asian-Americans. Harvard and other elite universities disgust me for several reasons:

1)The whole reason IQ is so fascinating to me is that intelligent people get to the top naturally by doing smart things & avoiding dumb mistakes. Elite schools demand that smart people get ahead by doing well on an IQ test ( SAT) that gives them credentials. This takes a fascinating natural phenomenon (smart people get to the top) & reduces it to a boring socially engineered self-fulfilling prophecy & prevents us from studying the phenomenon under ideal circumstances. It’s like trying to study why the fastest cheetah gets the food only to discover someone has been testing the cheetahs for speed & feeding the fast ones instead of letting them catch food themselves.

2) Elite schools are full of hypocrites. They claim to be liberal and anti-HBD, yet they use a disguised IQ test (the SAT) as a major factor in selecting students. If that weren’t hypocritical enough, they then cherry pick from the high scoring population which students to select based on arbitrary and suspicious criteria.

3) I’m a proud Canadian. In Canada, there is no Ivy League. Here anyone can get ahead naturally through hard work, ambition, luck, and smarts. We’re not branded for life based on where we went to school at age 20. The American Ivy League thinks they’re a meritocracy but they’re largely a caste system, and graduates go out into the word and actively discriminate against people who went to lesser schools. If you look at the people who write for America’s most influential newspapers, work for America’s most lucrative investment banks, and fill influential positions in the white house, graduates of elite schools are dramatically over-represented, even after controlling for the likely IQ distribution of such occupations.

4) Ivy League schools destroy the fabric of America. If scholar Charles Murray is correct, back in the 1950s, the U.S. used to be a lot like Canada. There were small rural towns in middle America where people with IQs of 130 and IQs of 70 lived as neighbors, each contributing their unique qualities for the good of the local community. But thanks to elite schools, the best and brightest in small town rural America are being removed from their communities where they did a lot of good and sent to places like Harvard where they are recruited into the largely useless coastal elite professions. Meanwhile the small town rural communities they leave behind suffer a brain drain and degenerate into an underclass (see Charles Murray’s book Coming Apart )

At first I was excited when I heard the recent news that president Obama had chosen a black woman to be the next attorney general, but in the back of mind I thought “please don’t let it be another Ivy League snob”. I immediately looked her up on wikipedia and when I saw that she was a Harvard graduate, I felt absolutely sick. The whole reason I cheered for a black man to be president back in 2008 was that I want to live in a less discriminatory world. President Obama has done a good job being more inclusive to women and minorities, but when it comes to being inclusive to non-Ivy Leaguers, his record is terrible.

The Wall Street Journal reports:

President Obama has six Ivy leaguers in the cabinet: Hillary Clinton (Yale Law School) at State; Tim Geithner (Dartmouth undergrad) at Treasury; Attorney General Eric Holder (Columbia undergrad and law school); Gary Locke (Yale undergrad) at Commerce; Shaun Donovan (Harvard undergrad) at Housing and Urban Development, and Arne Duncan (Harvard grad and undergrad) at Education.

President Clinton had five: Defense Secretary Les Aspin (Yale undergrad); Attorney General Janet Reno (Cornell); Interior Secretary Bruce Babbitt (Harvard Law); Labor Secretary Robert Reich (Dartmouth and Yale), and HUD Secretary Henry Cisneros (Harvard graduate school).

By comparison, George H. W. Bush, and George W. Bush had four each.

One of the best things about Canada is we don’t have anything equivalent to an Ivy League. Some universities here are more prestigious than others, but the differences are small, elusive and inconsistent and no one here much cares which university one went to. But in America, it’s a caste system where the Ivy League looms large, and Ivy Leaguers seem to view themselves as some sort of superior ruling class, and when they get into power, they appoint other Ivy Leaguers to positions of influence. And nowhere does this trend seem more pronounced than Washington, where all of the last four presidents have been Ivy Leaguers, and if Hillary Clinton gets elected, that’s an astonishing five in a row.

Part of the enormous overrepresentation of Ivy Leaguers in the white house is that the presidency selects for ambition, IQ and family wealth (all of which are strongly correlated with an Ivy League education) but the overrepresentation of Ivy Leaguers seems to be getting worse, so I can’t help but wonder if a lot of it is outright discrimination against anyone who didn’t attend the right school by various gatekeepers to power.

It will be interesting to see if the republicans oppose President Obama’s choice for the next attorney general. If they do, it will look like they are opposing her because she’s a black woman. If they’re smart they should go after her for being another Ivy League grad and ask Obama why he can’t pick an African American who didn’t attend an elite school, something blogger Steve Sailer has criticized him for.