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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.
Brain Size 
It wasn’t the original WAIS, it was I believe an abbreviated version of the WAIS-R (that used only the Vocabulary and Block Design subtests). The ceiling for both subtests is 145 for a composite ceiling of about 150.. That’s an extremely high ceiling though perhaps not high enough for many at Harvard. But test scores correlated with real life creativity all the way up to IQ 150 showing the test had predictive validity all the way to the maximum score.
On the other hand, the WAIS-R was normed around 1981 and the Harvard students tested around 2000, so one could argue the scores were too generous because of old norms.
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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/
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
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.
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.
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.
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.
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. 🙂
98% of Harvard and 50% of MIT flunked a defense Dept. test that exempted those who ;passed the test from the VietNam draft.
Ignore that last “because” in my last response. I was going to formulate that sentence differently.
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.
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.
Mathematical results that are consistent with the empirical does not mean that the method used to obtain them is reasonable!
John is completely right. Your “good results” are accidents, as is your 147 IQ average.
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.
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.
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.
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.
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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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.
There is a bigger problem: The author has confused correlation coefficients with regression coefficients. Multiplying by the correlation coefficient doesn’t make any sense.
When two variables are converted to the same normalized scale, then correlation coefficient = regression coefficient.
Hey Derick, your comment that ” The brightest people in the world are university drop outs who realize that institutional education is about conformity” seems to agree with UC Davis’ professor Dean Keith Simonton’s research. You may wish to read his 1984 relative book “Genius, Creativity and Leadership”: most eminent scientists did not obtain a graduate degree. They were graduate school drop outs, not generally university drop outs. I read this book during the spring quarter of my first grad year at UCLA (1988-89), coincidentally when I had just decided to drop out of the Chemical Engineering doctoral program and settle for an MSc degree (simply in order not to carry eternally the stamp of “looser”; I didn’t like the life in America and I left for ever after getting my Master’s). Of course, I never became one of the most eminent scientists in the world, either!!
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.
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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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.
Good points. There’s a lot of debate about the issues you raise.
You have the guts to respond to even gulls and/or envy-torn guys. Congratulations 🙂
A real IQ test is constructed of pure reasoning: 1) matrix reasoning and 2) spatial reasoning. The most crucial is matrix reasoning because this is logical problem solving. Spatial reasoning came in later and is an additional ability that carries a strong environmental component which can be both raised and reduced, though matrix reasoning is truly inherited via genes. Problem solving is essential to life itself, as life is filled with all kinds of problems, from personal ones to societal ones. We’ve been problem solving since the birth of our species. Human beings problem solve their way to obtaining true knowledge and applicable skills. It is the deepest, most efficient form of learning. I know from personal experience being a gifted problem solver myself. It does not have to be maths because anything which is comprehensible to the brain equates to problem solving (trust me).
Some folks call it ‘critical thinking’ but they mean the same thing as logical analysis. What you’re doing is abstracting the information from something, anything, perhaps the environment itself, and analysing all the many details you see/hear/feel/smell/taste, then you are meticulously separating the significant details from the trivial details. The significant details eventually form a pattern thus leading to intellectual enlightenment. It’s awareness! This is how the brain comprehends anything of significance. There’s just no better and more natural way to learn, for we evolved to do it!
Standardised tests and verbal tests are quite trivial due to the large educational dependency and overused rote learning or memorisation, which is more to do with obtaining surface-level academic skills than using deep-level raw intellect. A person with more raw intellect is always technically more capable of doing complex theoretical work, and this can’t be dismissed. No amount of literacy and numeracy will give you a sophisticated mind. You’re limited by your logic, especially if it is poor. There are indeed ‘educated people’ with poor logic. The academic delusion is based upon the false belief that obtaining surface-level academic skills makes a person intelligent when, in reality, such persons could have a serious lack of logic in their brains. The refusal to accept the importance of logic is an essential part of the academic delusion. Almost no psychometrician or psychologist wants to address the importance of logical problem solving in our daily lives.
The ‘g’ factor is a statistical myth born from the academic delusion. The ‘causation’ of the correlations between subtests of standardised testing is short-term memory rather than IQ (problem solving). We know this because rote learning predominates. More often than not a person is learning by rote rather than actually problem solving. There is every reason to believe that short-term memory is crucial to rote learning, and therefore crucial to academic success. Regardless of a person’s IQ (problem solving), if they don’t have a sufficient short-term memory, they will struggle to learn by rote.
There are many individuals with an odd combination of very high IQ (problem solving) and a weakened short-term memory. We are the intellectually gifted. We tend to have ‘attention problems’ and acute sensitivity. Nobody knows exactly why this is the case but the sad fact is: the intellectually gifted are being buried beneath the statistical myth of ‘g’ and are being replaced (insidiously) with imposters which have the nerve to think of themselves as ‘superior’ for no good reason. The ‘g’ factor is a dangerous delusional belief, especially towards the intellectually gifted but also towards poor people and society as a whole.
Hey VoiceOFReason, hi again. I have two questions after reading both comments of yours in this forum:
a) GMAT, a standardized therefore quite trivial test according to your beliefs, incorporates a section called “Critival Reasoning”. If you are familiar with this test and specifically this section, do you think that it is useless in measuring logical problem solving ability, which I understand is the only important intellectual ability for you?
b) Raven Progressive Matrices, which you accept perhaps more than any other IQ or “IQ” test per your earlier comment at the bottom of this page, is designed to measure “g”, according to the designer and his descendant (Cognitive Psychology 41, 1–48 (2000): “The Raven’s Progressive Matrices: Change and Stability over Culture and Time”, John Raven (page 2)). Since you believe that the concept of “g” is a statistical myth, was J.C. Raven unsuccessful in his effort to measure “g” (if it really exists) with his tests? In other words, did he start trying to measure “g”, but ended up in measuring something still important, but different than “g”? Like Columbus, who started to discover the western way to India, but ended up discovering America?
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.
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.
Cal Tech had the highest IQs in the world.
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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.
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.
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.
The MIT physics department would like a word.
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.
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
The 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.
Wouldnt variation around the slope imply nonlinearity?
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).
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.
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).
Hi Pumpkin Person. I have read quite a few of your essays and I admit I find them very interesting, as they help me learn some rare data I wasn’t aware of (e.g. SAT statistics for the general, not college-bound US population of young adults etc). I also find inventive the ways you reach to conclusions and therefore, I subscribed to your blog.
However, the present essay troubled me from the first lines I read, for the reason that has instigated the main controversy above, i.e. the controversy regarding correlation and regression. As I had my last Statistics course in 1992, I reverted to the relative notes I had kept since since then, i.e. since I did my MBA at the Imperial College. After some reading, I simply copy a small passage that clarifies the matter:
” ρ = +/-1 indicates a pure linear relationship
ρ = 0 indicates a lack of any linear relationship”,
and I add the evident, i.e. that an absolute ρ value between 0 and 1 indicates a not precisely linear relation (ρ is the real value of the correlation coefficient, which is in practice approximated by r, the product moment correlation coefficient).
Therefore, Richard M Boyer and the people who agree with him are correct: the correlation coefficient defines the linearity or non-linearity of the relationship. The regression coefficient, on the other hand, defines the slope. Two relationships may both be perfectly linear, i.e. have correlation coefficients equal to 1 (or -1), but different slopes, i.e. different regression coefficients.
When does the correlation coefficient equal the regression coefficient? When the value of the dependent variable (i.e., the one that is not controlled but observed, value-wise, after varying the independent one) is constant. Then, both coefficients are equal to zero.
This is what I understand having just went through my old Statistics’ notes. Although I use my real name, I won’t be rancorous to anyone who might correct me. On the opposite, I welcome knowledge.
Hey Pumpkin Person, hi again. I was thinking of the above issue (regression Vs correlation), so I just revisited this page. Therefore, it is only a few minutes ago that I paid due attention to the following comment of yours:
” When two variables are converted to the same normalized scale, then correlation coefficient = regression coefficient.”
So, I’m thinking that indeed “normalization to the same scale” may make the difference so you may be right. I furthermore assume that normalization to the same scale (e.g., a percentile or, equivalently, a rarity scale, something that is quite commonly done in IQ and psychological cross-standardizing) can be done for any two sets of data. What I understand that you are doing in your above artcile, is the assumption that not only IQ, but also the other variables you (cor)relate with IQ are normally distributed and, as such, they can be treated as being on the same with IQ percentile (or rarity, or z) scale.
I am almost convinced. Still, could you:
a) Refer me to a statistics’ article proving or simply quoting the equality of the correlation and regression coefficient of two normalized to the same scale data sets? My intuition doesn’t seem to help me.
b) Were Daniel Seligman’s data sets, i.e. IQs and elementary school grades, which had a 0.65 correlation coefficient, normalized to the same scale? If not, would the correlation coefficient change, in case these data sets were adjusted per above?
c) Finally, a stupid question: if we take all the above as true facts, why do you assume that IQ = 0.65 x (normalized criterion) + C1 and not that (normalized criterion) = 0.65 x IQ + C2, whereby IQs would of course skyrocket? Is this given by Seligman?
Thanks.
I just read the relevant appendix C, “Structural Equation Modeling”, of D.K. Simonton’s book “Genius, Creativity and Leadership”, published in 1984 by Harvard University Press. To use Simonton’s terminology, the “causal” variable is IQ and the “effect” variables are elementary school grades, Harvard admission, becoming a tenured university professor and becoming a Nobel laureate. The regression coefficients show simply how many SDs above or below the mean the “effect” variable will be for every SD above or below the mean the “causal” variable is. Therefore, per question c I asked above, IQs should be higher than the ones predicted: Δ(normalized criterion) = 0.65 x Δ(IQ), or Δ(IQ) = 1.54 x Δ(normalized criterion), which seems very reasonable to me. Some intellectual ability of a genius goes astray to other trite endeavours compared to winning the Nobel prize, for instance.
IQ is not learned academic skills. If it was then it wouldn’t be legitimate because the effort (or lack thereof) of children would manipulate the outcome. Here’s the problem. At aged 17, I was semi-illiterate. At aged 27, I am a skilled fiction writer and essentially ahead of my generation. I’ve got the structural tools of someone in their late 30s/early 40s. At aged 17, I was assumed ‘not the brightest’ simply because I was semi-illiterate at that point in time. This is completely wrong. I possess a large capacity for abstract thought and was competent enough to teach myself how to write and edit. I also learned very quickly thus leaping ahead. IQ is abstract capacity, a legitimate measurement of intellectual potential. Intelligence is thought complexity, which is essential to many domains, crafts and vocations. It doesn’t matter if you’re a fiction writer or a bio-chemist; you’re not getting very far without a good deal of abstract thought.
It’s disgraceful that they’ve been studying intelligence for about 100 years and most academics STILL don’t get it. A child with a large capacity for abstract thought is much more capable, even if they struggle to pay attention in school and get Cs/Ds. When that child is an adult man or woman they will be MANY TIMES more capable. A person with an average-sized abstract capacity has NOWHERE NEAR the potential of a person with a large abstract capacity. It’s the objective truth.
Learned academic skills can only get you so far in life, you need abstract thought as well. People can always improve on their academic skills, simply by using them every day and thus reaching higher levels of literacy and numeracy because it is a practice after all, though what people can’t do is increase their abstract capacity. And by abstract, I mean LOGIC/PATTERN RECOGNITION. Those who are truly limited are those with a small abstract capacity. In fact, they are mildly mentally retarded. Again it’s the objective truth. One of my cousins (aged 28) suffers with mental retardation and he has low pattern recognition, which was tested twice over and in a very professional fashion. It makes sense since his logic is very poor and he can hardly engage in mature conversations. His thinking is too childish for him to understand much of anything. This means a very important thing: the smaller the abstract capacity the younger the mind, the larger the abstract capacity the older the mind.
The ultimate conclusion is that pattern recognition is the MAJOR FACET in IQ. Abstract capacity is not merely the ability to learn skills; it’s the ability to conceive of complex ideas, to think on a higher plane, to think in very sophisticated ways. This is REAL intellect.
So, if IQ is abstract capacity, it is indeed important.
When we make IQ about academic skills we trivialise it, therefore ruining the concept of IQ. People will argue that everyone just needs to ‘work harder’ and the difference won’t matter. This is WRONG. A person with a small abstract capacity is challenged in all sorts of ways and nothing is going to change it. Even if they work very hard and achieve more than what we expect from them (academically), they still think like children and won’t engage in mature conversations. It’s not even their fault but it’s still problematic. Some of them ARE literate but have nothing significant to say. Their understanding is too poor. Even as adult men and women they talk/write about all the trivial and simplistic things in life, which is a reflection of how infantile their minds are.
The REAL IQ of the ‘average’ academic is perhaps between 100 and 110 i.e. slightly above-average but not particularly competent. That is a pattern recognition score between 100 and 110. It explains why so many academics are hopeless at their jobs and why half of them want sacking. My pattern recognition score is 135 i.e. significantly above-average, and I’m a fiction writer not an ‘academic elite’. Pattern recognition is REAL IQ. Leading researchers and top scientists possess much higher pattern recognition than the average mediocre researcher and scientist. Scrap the rubbish, low quality, highly inaccurate, meaningless and trivial standardised tests and REPLACE them with a far more specific test: Raven’s Matrices. This test aims to measure the speed AND sophistication of the brain. In other words: LOGIC. Academic selection should be (ideally) based upon the principle of which brains are hardwired for logic. We’re extremely competent at solving complex problems and discovering NEW knowledge, and we constitute perhaps 10% in the western world. Allowing a good 5% of us to fade away is AWFUL.
I hold Americans primarily responsible for the complete perversion of IQ. If they weren’t so utterly obsessed with trying to ‘prove’ the inferiority of blacks, women and poor people, then they would never have perverted IQ to the extent that they have. This is a sham and also a tragedy since many intellectually gifted children disappear off the radar generation after generation. America is busy shooting themselves in the foot, since ‘proving’ that blacks, women and poor people are inferior is FAR more important to them than discovering which of their children possess REAL intellectual potential.
Pattern recognition/logic/abstract capacity = REAL IQ.
Standardised test/academic achievement = FAKE IQ.
Intelligent academics are intelligent IN SPITE of their degrees and NOT because of them. It is absurdly arrogant for an academic person to think of themselves as ‘intelligent’ just for earning a degree or two or three. They call this ‘proving themselves’ do they? An intelligent academic is far more inclined to EXPRESS their intelligence by the creation of original work. When judging intellect: we always must go by the thought complexity in the work. Intelligent people produce things of good quality and significance. There ARE certain academics I respect…though many of them need not pulling down, but tearing down from their high horse…and the ‘common person’ is just the one to do it.
If any ‘academic elite’ with a hot temperament and an arrogant flair wishes to argue with me then bring it on. We’ll see how clever you are via your own reasoning. Come and ‘put me in my place’.
Now I’ve SOLVED the problem of IQ.
Hello VoiceOFReason. I read your comment above and I agreed with almost every single word you wrote, but mostly with your belief that “real”, as you call it, IQ does make real sense. At last, someone who is not afraid of stating that (real) IQ is something that differentiates people, irrespective of their “success” in life.
I would, related to the above, appreciate it if you could share with me any data you might have on academics’ RPM or, better, RAPM scores. I want to show it to the most idiotic person I have met, a Ph.D. holder in a non-existing discipline, imho. She totally despises IQ, perhaps because her’s is evidently below average.
I think you’re using the correlation with ELEMENTARY school grades and iq far too liberally, especially in applying it to iqs of nobel laureates. If the inappropriateness of doing such a thing isn’t obvious, then I don’t know what to tell you
i admit it’s speculative.