**Tags**

Anne Roe, correlation, education level, grades, Harvard, IQ, Nobel prize, PhDs, professors, SAT

In the book,* A Question of Intelligence* by Daniel Seligman, he reports (pg xiv) that the correlation between IQ and elementary school grades is 0.65. This correlation is far from perfect since how hard you work is just as important to grades as how smart you are, but the correlation is still very high (as high as many IQ tests correlate with each other). The correlation drops in high school and drops further in university, but that’s probably because as you move up the educational ladder, a lot of low IQ people drop out, so there’s less IQ variation for grades to correlate with. But in elementary school, you have virtually the full range of cognitive ability, so it’s a good place to understand the true relationship.

So in a typical elementary school class, you might have 30 students, which means that the lowest IQ in the class should be 28 points below average and the brightest in the class should be 28 points above average (IQ 72 and 128 respectively). However because IQ and grades “only” correlates 0.65, the best and worst students in the class should have IQ’s only 65% as extreme: 82 and 118 respectively.

Of course, elementary school grades are only one way we can quantify academic success in the general population. Another way is years of schooling or highest degree obtained. In the U.S., a PhD roughly marks the top 1% in years of completed education, which suggests that the median PhD is in the top 0.5% in education level. If there were a perfect correlation between IQ and academic success, we’d expect the average PhD to have an IQ of 138 (the top 0.5%), but since the correlation is “only” 0.65, each point above 100 must be multiplied by 0.65, reducing the average PhD to their actual IQ which is around 125 (still very high!).

**IQ’s of Harvard students**

Are there academic achievements more impressive than getting a PhD? Yes. Getting acceptance into Harvard: the world’s most prestigious university. Out of the 4.1 million 18-year-olds in the U.S. in a given year, only about 1600 go to Harvard. So if there were a perfect correlation between IQ and academic success, the dumbest Harvard student would have an IQ of 150 and the median might have an IQ of 153. However because the correlation is only 0.65, the median Harvard student should be only 65% as far above 100. Thus, simple regression predicts the typical Harvard student should have an IQ of 134. Actually a sample of Harvard students studied by Harvard psychologist Shelley Carson and her colleagues scored somewhat lower on an abbreviated version of the Wechsler intelligence scale:

Eighty-six Harvard undergraduates (33 men, 53 women), with a mean age of 20.7 years (SD = 3.3) participated in the study. All were recruited from sign-up sheets posted on campus…The mean IQ of the sample was 128.1 points (SD = 10.3), with a range of 97 to 148 points

On the other hand, the average Harvard student has an post-1995 SAT score (reading + math) of 1490, which according to my formula equates to an IQ of 141.

The SAT likely overestimates Harvard intelligence because when you select people who did especially well on one test, you are also selecting people who got lucky, were well prepared and overperformed on that one test. Such people will likely regress to the mean when given a test that wasn’t used to select them. On the other hand the abbreviated WAIS may have underestimated Harvard students because it’s a very brief test, and thus gives only rough results. Averaging their scores on both tests, gives an IQ of about 135. Almost identical to what simple regression predicted based on the 0.65 correlation between IQ and academic success.

**IQ’s of tenured professors**

Another form of academic accomplishment that’s about as exclusive as attending Harvard is becoming a tenured university professor. Scientist Steve Hsu wrote:

…when an attorney prepares a case it is for her client. When a Google engineer develops a new algorithm, it is for Google — for money. Fewer than one in a thousand individuals in our society has the privilege, the freedom, to pursue their own ideas and creations. The vast majority of such people are at research universities. A smaller number are at think tanks or national labs, but most are professors…

So in terms of academic success, being a full tenured professor is a one in thousand level accomplishment. If there were a perfect correlation between IQ and academic success, the dumbest tenured professor would have an IQ of 147, and the average tenured professor would probably be around 150. But since the correlation is 0.65, we should expect the average tenured professor to be around 133 with quite a bit of variability around that mean, depending partly on the prestige of the university they teach at and the g loading of the subjects they teach.

**IQ’s of Nobel Prize winners**

Are there academic accomplishments more impressive than becoming a professor or going to Harvard? Yes: Winning the Nobel Prize. Many years ago a respected psychometric expert named Garth Zietsman wrote an article about using this type of regression to estimate the IQ’s of Nobel laureates, though I don’t remember the exact stats he used.

But let’s say only one in a million American adults has a Nobel prize (excluding the Nobel peace prize which is non-academic). If there were a perfect correlation between IQ and academic success, we’d expect the dumbest American Nobel laureate to have an IQ of 171 and the average Nobel laureate to be around 174. But again, since the correlation is 0.65, the average Nobel laureate should have an IQ of 148, or roughly 150 if you like nice round numbers. Of course there would be a lot of variability around the mean. Those who earned their Nobel prize in hardcore intellectual subjects like physics would likely average above 150. Those who earned their prize in more subjective and artistic subjects like literature would likely average well below 150; indeed probably below 140.

Is it plausible that the average academic Nobel prize winner has an IQ around 150? Yes: In the early 1950s, Harvard psychologist Anne Roe intelligence tested extremely eminent scientists who were very close to Nobel Prize level. She found they had an average Verbal IQ of 166, an average Spatial IQ of 137, and an average Math IQ of 154. These are very inconsistent results suggesting there might have been problems with how the tests were created and normed. Nonetheless, if you average the three scores to cancel out the error, you get an IQ of about 150.

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John

said:Man. This “analysis” is just plain stupid. For one, Harvard isn’t necessarily the most competitive university. See the below link. You made the assumption that the 1600 people who went to harvard are the 1600 brightest students… which is plain laughable! And then gave them IQ scores that correspond in rarity to the likelihood that a given student of that age ends up attending Harvard. Honestly…

You could say the same thing about MIT, “those students are in the 1XXX/4100000 people in the nation, intelligence-wise!” And then you could say the same thing about U Chicago, Princeton, Yale, all all of those top schools (with similar SAT scores). And you could say the same to a slightly lesser extent for the top 50 schools, etc.! At that point, you’d have a heck of a lot of students that are all within that 1XXX/4000000 of intelligence given a perfect correlation. The backbone of this article relies on rarity of school attendance. What is the odds that someone ends up attending that school, rather than what are the odds that a person has a given intelligence level…

The premise of this whole article would be more realistic if you instead used “… got a 34/1500 on their ACT/SAT,” rather than “got acceptance into Harvard.”

http://www.forbes.com/sites/schifrin/2014/08/04/top-100-sat-scores-ranking-which-colleges-have-the-brightest-kids/

pumpkinperson

said:I never said they were the 1600 brightest, I said they were the 1600 most academically successful of their cohort (they made it to the most prestigious university).

I then calculated what their IQ would be if there were a perfect correlation between IQ & academic success. But since the true correlation is far from perfect, I regressed it to the mean

John

said:I realize that, but you gave them a IQ percentile based on your guess that those 1600 at Harvard are the top 1600 most academically successful in the nation, and used that as a basis for your calculations… the 1600 Harvard students =/= the 1600 most academically successful in the country anymore than the XXXX at Princeton or the YYYY at MIT. You know what I’m saying? So you can’t say that because the 100*(1-1600/4100000) is the percentile for those at harvard without assuming the same for those at Yale, MIT, Princeton, WashU, UChicago, etc.

pumpkinperson

said:But Harvard is more prestigious than the other schools you mention so it seems reasonable to define Harvard students as the 1600 most academically successful; at least by one definition of academic success.

But you’re right that the difference between Harvard & other elite schools is probably too close to call, so calling Harvard students the most academically successful is simplistic…but for the purpose of a simple analysis, it worked well and gave good results.

John

said:Harvard is more prestigious in your opinion. To the contrary, not everyone agrees with that, and the ones that are quickest to agree with that would be the average citizen who really doesn’t know what types of things ought to earn prestige. Therefore, only those who have opinions that are actually semi-educated should carry any weight. Just like you wouldn’t rank medical residencies’ prestige based on the general population’s knowledge of them.

If you look at people with 29+ on their ACT, they will probably have a different likelihood of citing Harvard as the most prestigious university than those who would score ~19-20, which is close to average in the general population. I think the best one could say about your analysis was that it truly was not very logical, but “hey, it gave the same results..” I mean to say that it is foolish to defend your math by saying that it gave the right answer. The same exact analysis would yield the same exact results for any of the top 5 colleges, which are also likely to be considered the most “prestigious.” In fact, some idiots would probably recommend their own state university as super prestigious (it might even be partially true, but not to the same extent), and even that university would yield the same results, if it has a similar student population. That doesn’t mean that there’s a glimmer of truth in their analysis, even a thread. No, not even a thread of truth must be present in order for a mathematical result to agree with an empirical result.

pumpkinperson

said:Regardless of who you polled, any credible study of college prestige would rank Harvard at or near the top. An average of all such studies would put Harvard at or near the top, so maybe my analysis had a pro-Harvard bias, but not enough of one to significantly skew the numbers.

Callitwhatyoulike... (@callitwhatulike)

said:Wanna know which school is the most prestigious? Ask someone who didn’t go to college (even better, someone who didn’t graduate from high school). You’ll hear Harvard, every single time. 🙂

David Disher

said:98% of Harvard and 50% of MIT flunked a defense Dept. test that exempted those who ;passed the test from the VietNam draft.

John

said:Ignore that last “because” in my last response. I was going to formulate that sentence differently.

John

said:Also, you made the assumption that grades are equivalent measures to what you are assuming is “academic prestige” i.e. you said that because ELEMENTARY school grades correlate .65 with IQ, that therefore the prestige of your college correlates .65 with IQ. I’m sorry to say this, but I have to tell you that your methodology is flawed. It isn’t flawed on “mere technicalities” but your entire premises are completely incorrect and your assumptions are somewhat absurd.

pumpkinperson

said:Academic success can be defined and measured different ways: grades, years of education, prestige of education, Nobel prize etc. Since two of these measures of academic success (grades & years of schooling) are known to correlate 0.65 with IQ in unrestricted samples, for simplicity I assumed that all forms of academic success correlate 0.65 with IQ. You can argue that’s too simplistic, but it seems to give good results.

John

said:Mathematical results that are consistent with the empirical does not mean that the method used to obtain them is reasonable!

Reply

said:John is completely right. Your “good results” are accidents, as is your 147 IQ average.

John

said:A better article would be based on something relatively standardized, for example, GPA (which would vary much between schools and between majors) or SAT/ACT scores. Like, counting the amount of people who score 34/1500 or higher on their ACT/SAT, multiplying this amount by some factor that takes into account that not all of the people who take these tests are seniors (the factor would be less than one), multiply this resultant number by some factor that takes into account that some people would have qualifying scores on both the SAT and ACT (multiply by a factor less than one) and then dividing that by the amount of people that are 18 years old. This would give you the relative intellectual rarity of the SAT or ACT in the general population with the assumption that the amount of people who are capable of scoring this high, but don’t take either of the tests (think high school dropouts) is negligible (or you can incorporate another factor less than one, probably higher than .95). Then you can determine whether this score is more rare than earning a pH.D, etc.

John

said:Oh yeah, I forgot to mention: OR you could simply define the academic success of those at Harvard to be the academic success of those with Harvard’s average SAT. You might add or take away a bit from that SAT score to correct for whether or not you think that they require more or less extracurriculars and other factors, but it wouldn’t be more than a .5 ACT difference from their average. It wouldn’t be more than .3 TBH. But their average ACT is 33.5, and maybe you could bump it up to 34 for argument’s sake. But then you’d have to determine whether or not a 34 ACT is more or less impressive than earning a pH.D, or what have you. By the way: it still would be more impressive, in terms of rarity in academic success, which could be called academic aptitude in this case. But assuming that those at Harvard is the top 1600 most academically successful students is simply wrong. This is almost equivalent to saying that those at Harvard are on average, equally academically successful as those with a 36 on their ACT plus the best of those with a 35.

pumpkinperson

said:I think you’re making it more complicated than it needs to be. When comparing getting into Harvard to getting a PhD, you’re comparing two different dimensions of academic success.

1) the prestigue of your education vs the length of your education

Harvard students are more rare on the prestige dimension than PhDs are on the length dimension unless you deny that Harvard’s the most prestigious university in America.

Megan

said:Pumpkin, did you go to Harvard? You have a tremendous inclination towards disregarding alternative ways of calculating to suit your own agenda, basically Harvard is great, wonderful, and PRESTEGIOUS. My goodness friend, perhaps you should also see the ethnicities and backgrounds of these students, it seems many if not most, will have the means to pay for Harvard and not use much financial aid. I agree with John, this is flawed in that 1600 get in each year, however, they can afford to go, financially or otherwise. These children may not have the responsibilities of others. To say what you are saying is mere opinion, which you are entitled to, yet do not confuse them with facts.

pumpkinperson

said:I’m Canadian & went to a university here; I think all Ivy League schools are disgusting.

The point was not to glorify harvard but to show the robustness of a simple linear 0.65 regression across diverse measures of academic success

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Derick Olson

said:The application of applying .65 to the assumption that the highest IQs are at University is entirely flawed. The brightest people in the world are university drop outs who realize that institutional education is about conformity. Professors are not in the top 5% of the brightest people in the world. Maybe they were 100 years ago, but not anymore.

Joshua Hartshorne

said:There is a bigger problem: The author has confused correlation coefficients with regression coefficients. Multiplying by the correlation coefficient doesn’t make any sense.

pumpkinperson

said:When two variables are converted to the same normalized scale, then correlation coefficient = regression coefficient.

tommydav

said:Actually, as unpopular as this might be, I’m with John on this one. The .65 correlation isn’t actually far off at all. If you read what psychologists have to say about IQ’s and correlations, you’ll find that they say that 68% of people would fall between the ranges of 85 – 115. So the actual number should be “.68” but John is still correct in stating that there would a consistent linear regression.

John

said:This is the same John. To clarify, I believe that a .65 correlation might be realistic for IQ and academic achievement tests (e.g. SAT or ACT), but not necessarily for academic prestige. For example, I do not believe that there is a certain point gap in the IQs between MIT and Harvard unless there is a corresponding change in average ACT/SAT scores. I think any significant correlation between prestige and IQ would disappear if you partialled out the variance due to the changes in SAT/ACT scores.

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Remy

said:The main flaw is in your presumption that natural intelligence is the main variable in determining traditional markers of academic success (e.g. test scores, GPA, et al.). Natural intelligence may be a factor, but it’s only one among many. The elephant in the room is parental income and more broadly, one’s childhood environment. Rich parents can afford to spend thousands of dollars in SAT tutoring to assure a high school. People from more disadvantaged backgrounds don’t have those kinds of opportunities. Many high academic achievers at IVY institutions tend to be people of average to slightly above average institutions who’ve been put through the saw mill by helicopter parents from the age of 4 onward. So the explanation for why the “smart” kids tend to be smart is often more nurture than nature, not that there aren’t exceptions to the rule, but we can’t deny the large role home environment plays in educational attainment. If we look at the plethora of Ivy league grads in arenas such as politics, media, and law, they’re hardly what one classify as ‘great minds’. Truly great minds tend to be ostracized and disenfranchised by mainstream society, which is why they gravitate towards creative fields, and some towards scientific research as well of course. And let’s face it, there’s little correlation between what we would class as “creative genius” and high academic achievement. Great artists can go either way. Faulkner was a state school dropout. T.S. Eliot went to Harvard. Terrence Malick was a Rhodes Scholar. Kubrick had a D average in high school. Many of the most intellectually gifted in this world do poorly in school, largely because they find themselves constrained by the rigidness of institutionalized education.

pumpkinperson

said:Good points. There’s a lot of debate about the issues you raise.

aranceelimoni

said:You have the guts to respond to even gulls and/or envy-torn guys. Congratulations 🙂

amays

said:The tile of the article aptly reflects the proposed discussion. Whether or not Harvard represents the most prestigious university is not significant as this is not a peer-reviewed journal offering irrefutable evidence of the author’s conclusion. Harvard is definitely one of the most prestigious university’s in the U.S. (arguing against that probably represents a stronger bias than placing Harvard at the number one position), and as such represents academic elite status. It is important to note that while factors such as household income of Harvard students is certainly a factor for admission and attendance, there is also a correlation between income level and IQ. The inclusion of other markers of “academic elite” status adds to the validity of the argument. If this were indeed a reputable, peer-reviewed journal, the only necessary change would be to identify the shortcomings (selection of only one university, lack of quantifiable prestige, etc.) and suggest the need for further research. It does not mean that the proposed idea is completely invalid. What would be interesting is to note what factors cause the correlation to be so low? Is there a reliability range in which the correlation rises? Would exceptionally high intelligence actually correlate with a lack of academic success, such as poor grades, dropout rates, etc.? Perhaps this has been done, but such a negative correlation would suggest the shortcomings of our current education system with meeting the needs and maximizing the potential of our most brilliant minds.

javadba

said:This article is crock. How can you simply multiply the correlation and make that the additive factor? That is by far the worst error. There are other issues such as claiming that Harvard students have the highest IQ (ever heard of Caltech?) The resulting IQ’s are generally too low vs the reality.

David Disher

said:Cal Tech had the highest IQs in the world.

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David Disher

said:My class at MIT ’65 had an average IQ of 150 while Harvard was at 135. SAT scores in verbal aptitude were equivalent but MIT was 100 points higher in mathematics aptitude. This was before affirmative action.

Bris Vegas

said:University prestige is based almost entirely on published research papers.. Research is mostly done by PhD candidates..Only about 5% of Harvard PhD mathematics and science PhD candidates were Harvard undergraduates. So Harvard’s prestige is primarily due to recruiting outstanding people who were educated at other universities.

Anthony

said:If we are talking about hard science (e.g. physics), IMO some or even most physicists would rank MIT or Stanford higher than Harvard. At least that’s how I would rate as a physics grad. Harvard is good for social connection and business, not necessary for science, the former doesn’t necessarily care as much as IQ than your social connections.

Eyesuck

said:The MIT physics department would like a word.

Richard M Boyer

said:This article does not seem to understand correlation. The article seems to treat it as a proportionality factor that can be used to adjust one random variable so as to be in alignment with another random variable. It is not, rather it is an indicator/measure of the presence of a linear relation or proportionality between two random variables. If the correlation is 1 then there is a precise linear relation between the random variables. If the correlation is .65 we do not have a precise linear relation between the random variables. To adjust one distribution by decreasing its values above the mean by saying multiply these values by the correlation value of .65 to bring it in alignment with the other distribution is treating the two distributions as being proportional or as having a precise linear relation which the correlation value of .65 is indicating is not the case. Please don’t do this, on the other hand you may be lucky and be spot on, but only by accident.

pumpkinperson

said:If the correlation is 1 then there is a precise linear relation between the random variables. If the correlation is .65 we do not have a precise linear relation between the random variablesThe linearity of the relationship is independent of the correlation. The only difference between 1.0 and 0.65 is not the linearity, it’s the size of the slope and the amount of variation around said slope.

symmetry

said:Wouldnt variation around the slope imply nonlinearity?

Nathan

said:Are you your reasoning for decreasing correlation is correct? I don’t think it’s due to fewer data points because of the n=30 rule and large population.

If the correlation decreases because the average student IQ increases, which is true given your statements, that implies a stronger relationship between low IQ and grades than high IQ and grades.

What I’m seeing is an inverse relationship on the correlation between IQ and IQ correlation with grades (as IQ goes up the correlation with grades goes down).

symmetry

said:While the average iq of any group is only a rough estimate of a norming, its calculation involves other numbers which are exact. Otherwise one could not arrive at a valid performance prediction for said groups. This is due to the fact that calculations of rough estimates alone only carry the avgs into obscurity.

Bruno

said:Pumpkin, all people criticizes you for under-estimating elite universities IQ, but I think, on the contrary, you overestimate it. If you take average SAT score at Harvard, Yale, Princeton, it’s 1 out of 200 among all people (ETS now calculate the % of users and for non users by testing all people from a certain age at comparing their results with users). But, that would give a 140 IQ, but with a correlation of 0.65, you get a 125 IQ. That’s 1 out of 20. HYP could select 1 people out of 2 000.

That means that for all people who are more intelligent than the HYP people (200K each year), only 1% ends-up at Harvard. It’s true that they take 10% of the high SAT scorers.

And as for top100 Universities, they take around 30% of the high scorers but only 13% of people above 125 IQ. People got confused because they think as the correlation among SAT and IQ were total (as I did myself before). And then, even when they realize, they don’t figure out the stat of admission.

The interesting consequences are :

– Murray is wrong saying that all intelligent people go to good Universities creating a new class based on intelligence. Only 10% of them do. And HYP take only 1% of the the intelligent people even if they represent half of the class in there.

– Claims that MIT average IQ (or Caltech, or Harvard) were in the 150 or 140 are completely false. It has never been above 125/130 IQ range

– A maximum of 20/30 person a year with an IQ above 150 go to HYP (cf. Gates comment). And probably 200/300 among all Universities. That’s enough for society to create knowledge. It’s really propable that out of the 120 people with IQ above 160, no one is admitted to HYP and very few into top100 one. And I guess many would drop out. So when people compares themselves to extraordinary able students there, it’s probably people with 150/155 IQ (not 165/175 IQ as in Allen and Co statements).