Saturday, September 21, 2013

Universities ranked by SAT/ACT scores

Jonathan Wai and Max Nisen rank US universities by student ability level as measured by SAT/ACT for BusinessInsider (methodology). Note I think using SAT/ACT disadvantages Caltech/MIT because the ceiling on the math component is lower than for the verbal, and many (almost all?) techers hit that ceiling. An alternative method using a higher ceiling test would yield improved rankings for STEM focused schools.

I always guessed that the Caltech undergraduate cognitive ability threshold was roughly few per thousand (perhaps even 1 in 1000) in the general population -- that's what the test scores imply. Although the kids are smart there is still a broad distribution on campus in the ability to learn core subjects like the required two years of math and physics (keep in mind -- these are Caltech-level courses!).

Based on my experience I would guess that the threshold ability to understand (for example) quantum mechanics is pretty high. A good chunk of the Caltech class doesn't grasp QM despite taking a year of it as sophomores -- and these are hard working, self-selected kids, in addition to being very smart. In our U Oregon study of psychometric thresholds, we found that kids in the top 1% of math ability (say, SAT-M > 750) had only a 50% chance of graduating in the physics major with more A's than B's -- i.e., in-major GPA > 3.5. Note, thanks to grade inflation the in-major average GPA in physics, as in other majors at Oregon and at other public universities (vs even higher averages at private schools), is something like 3.2, so 3.5 is not a high threshold (about +0.5 SD).

In other words, asking someone to explain Schrodinger's equation and the two slit experiment to you is probably a better verification of high end cognitive ability than any standardized test. (I wrote verification because understanding of QM is a sufficient but not necessary indicator of brainpower... some very smart people never study QM ... too bad for them!)

Here's what Vernon Smith (Nobel Prize in econ; started as a physics major at Caltech but bailed into EE and then econ ;-) had to say:
The first thing to which one has to adapt is the fact that no matter how high people might sample in the right tail of the distribution for "intelligence," ... that sample is still normally distributed in performing on the materials in the Caltech curriculum. The second thing you learn, if you were reared with my naive background, is the incredible arrogance that develops in conjunction with the acquisition of what you ultimately come to realize is a really very, very small bit of knowledge compared with our vast human ignorance. ... the difference between Harvard and Caltech: "At Harvard they believe they are the best in the world; at Caltech they know they are the best in the world."


coldequation said...

ISTR that back in the my day (high school class of '93), when almost nobody topped out the SAT due to the tougher scoring system, caltech students were tops and MIT was second. The most striking thing about this chart to me is that the Ivies now beat MIT now and nearly match caltech. This could be due to changes in scoring as you mentioned, or due to declining prestige of science and technology as it becomes more immigrant-dominated.

Douglas Knight said...

1. This is the average of the 25th and 75th percentiles. If you want to avoid upper censoring, use the 25th percentile (no, it's not 800). Caltech, MIT, Princeton, Harvard: 1490, 1410, 1410, 1390. (Completely ignoring ACT)

2. Since the 25th and 75th percentiles are the main numbers publicly available, it is widely reported that schools game them. It's plausible that the median at MIT is much higher than Princeton, despite the 25th and 75th percentiles being the same. And maybe the Caltech-MIT gap widens at the median. 10th percentiles probably vary widely.

3. Here is a graph from a paper (p 7/8) claiming odds of admission as a function of SAT percentile at four schools. It isn't monotone. I'm not sure what it means. Not knowing how many apply limits its usefulness.

Yan Shen said...

"Since the 25th and 75th percentiles are the main numbers publicly available, it is widely reported that schools game them"

Scores from publications like US News, etc are probably a bit on the high side...

"Last year the New York Times and the Chronicle of Higher Education reported that Richard C. Vos, a senior administrator at Claremont-McKenna College had falsely reported median student SAT scores to the Federal government, U.S. News and other sources since 2005. Bucknell University (PA), Emory University (GA) and George Washington University (DC) are among the other universities that have misreported such data.

Sharing an e-mail sent to the campus community, Clarement-McKenna president, Pamela Gann, told both media channels that the 25th percentile SAT score for the freshman class that entered in 2010 had
been reported as 1410, when it should have been reported as 1400. The 75th percentile score was reported as 1510 when it should have been reported as 1480.

Why would a vice president at one of the nation’s leading liberal arts colleges, among the top 10 to 15 schools, lie like this?

To advance the school’s rank in U.S. News?"

Douglas Knight said...

Oh, yeah, I meant to include another bullet point that these are self-reported numbers and might be fabricated. But that's separate from gaming, by which I mean that these two numbers may paint a misleading picture of the overall distribution of scores. Schools may care about some applicant scores only through their effect on these two numbers.

LondonYoung said...

You are becoming a softie in your old age Steve, going too easy on people now. Let's consider what it is to "deeply grasp QM". I would define that as the ability to participate in a meaningful debate on the interface between QM and classical observations ... to have a robust opinion on whether or not "many worlds" is the truth, or a cop out. I might even toss in the ability to respond to the question "hey, why do the 2s and the 2p orbitals of the hydrogen atom have the same energy, why should that be? accidental degeneracies don't just happen, you know".

steve hsu said...

Good point -- I removed the modifier "deeply" :-)

Diogenes said...

100 pts has to be subtracted for pre-recentering, unless the elites have become much more competitive in the last 13 years or whatever.

"Note, thanks to grade inflation the in-major average GPA in physics, as
in other majors at Oregon and at other public universities (vs even
higher averages at private schools), is something like 3.2, so 3.5 is
not a high threshold."

Yet American schools still use grades in making admissions decisions.

"In other words, asking someone to explain Schrodinger's equation and the two slit experiment to you is probably a better verification of high end cognitive ability than any standardized test."

That was a joke right? I hope so. SE and two slit are basic. I remember a professor of mine telling me abstract algebra could be more difficult than analysis because it was never clear what it was about. That is, the concepts were too abstract. Whatever. Algebra is waaaaaaaaaaaaaaaaaaaaaaaaay easier than analysis.

David said...

The median Caltech student is smarter than the median Harvard undergrad since the former doesn't have a special admissions process for legacies, minorities, and athletes (or at least not to the extent of Harvard and the ivies). I still think the top 5% of Harvard undergrad beats out the top 5% of any college in the world, in terms of pure talent. The IMO medalists, Intel finalists, Siemens Westinghouse winners, and other high-achieving teens flock to Harvard.

Iamexpert said...

Or the immigrants at MIT might be under-performing on the verbal SAT because English is a second language

Diogenes said...

Isn't Ito's lemma above the SE?

The fraction of the human race capable of understanding heidegger or hegel is even lower.

Diogenes said...

"In other words, asking someone to explain Schrodinger's equation and the two slit experiment to you is probably a better verification of high end cognitive ability than any standardized test."

And the absurdity of g at high level is made apparent by the following anecdotes. I knew a prof of theoretical chem who'd gotten a D in o-chem. I knew an md who found o-chem easy but found p-chem very difficult. And both were Jewish.

Iamexpert said...

Harvard might have the most geniuses per capita of any school in the world, but even at Harvard, one in a 1000 minds (IQ 147+) are rare on official IQ tests (not college admission tests where they score high by definition):

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.

Diogenes said...

"on official IQ tests"

that should have been "on an official iq test"

what was the iq test? it's no escret that self-described iq tests correlate with one another no better than the sat etc correlate with them.

Paul said...

I agree with your comment on Harvard, and would add that the top ~10% at HYPSMC are probably similar in cognitive ability. But if I were looking for the most intellectually remarkable 18-22 year olds in the country, I would begin my search at Harvard.

Diogenes said...

Washington is a good school, but it looks like it might be selecting for SAT more than the others. So if you've got little else but a high SAT, apply to Washington?

Or maybe most of its applicants take the ACT, and only the best even take the SAT.

Yet Reed's endowment is twice Mudd's and Tech's dwarfed by the others. The American class system is very much La Cosa Nostra.

Diogenes said...

"(no, it's not 800)"

was the math section even affected by the recentering and other bs? an 800 on the sat math was very unusual when i sat for it. 770, 780 were common enough at my hs, but i don't remeber any 800s.

Cornelius said...

The SAT should have a test of spatial ability as well. Engineering schools would benefit greatly from such a test, as would the students considering careers in engineering.
Unfortunately, we tend to push kids with high M-IQ into STEM majors, but we really should distinguish between those students with high S and those with low S. Students with high M but low S tend to have high V and are better suited for non-engineering STEM majors. High S, low V types seem to make the best engineers and experimental physicists.

bg2b said...

I wonder if that fraction included Heidegger and Hegel?

Kris Roys said...

The methodology is a joke. As you know, it's important to distinguish between mean and variance. Does anyone think based on the evidence that Harvey Mudd, Washington U, and Columbia are producing the BETTER graduates (the ones most likely to effect change) over Stanford as an example?

It's clear how proud you are of your alma mater, but this study is not one to make your case as a rhetorical point or future google link for some college student.

steve hsu said...

Class sizes vary quite a bit. Top 5% of H is almost 100 people whereas top 5% at Caltech is only about 10. I guess I'd say the quality of the latter group is higher.

If you were to say that the top 5-10 kids in a graduating class at H are as good or better than the top 5-10 in any other class then I would probably agree with you. Note, though, that recently MIT has been getting a lot of the IMO kids. I also suspect the top 5-10 at Tsinghua or the University of Tokyo are pretty good ;-)

steve hsu said...

Re: Ito, yes, but many more people get at least some exposure to SE or two slit experiment.

The two slit experiment is elementary, but still mysterious, and many people (including most scientists and some Caltech sophomores) would have trouble explaining it and answering detailed questions.

BobSykes said...

On the other hand, the graduates of these schools sacrifice children for work (Moloch?). So clearly, in Darwinian terms high IQs are dysgenic, and these individuals have lower fitness than welfare mothers.

It takes at least 3 children reaching adulthood to maintain a family line. Two is below replacement and leads to family extinction.

B.B. said...

Someone with an IQ score of 97 got into Harvard?

Iamexpert said...

The test was an extremely g loaded abbreviated version of the WAIS that used just the Vocabulary and Block Design subtest (at the time, the most g loaded verbal and non-verbal subtests respectively). Yes the SAT is also very g loaded...this study is not an indictment of the SAT, it's an indictment of the circular logic people use in measuring a population's IQ by the very test that defines that population. You can't use the SAT to measure Harvard's IQ, because Harvard students BY DEFINITION, overperformed on the SAT on average, and by definition, are brilliant at reading and math, so to do a truly independent auditing of their cognitive function, you need a statistically neutral test. If admission to Harvard were instead based on the WAIS, then the WAIS would be an inflated measure of their IQ's and SATs would give a more realistic value. Similarly, if I wanted to know the average IQ of Jeopardy champs, I wouldn't quiz them on general knowledge, even though general knowledge is highly g loaded, because Jeopardy champs are pre-selected to be brilliant at general knowledge so it's not a random sample of their brain's ability.

Iamexpert said...

Of course they do! If Tyrone Curtis Bogues, can get into the NBA with an HQ (Height Quotient) of 60, then we should expect people with IQ's below 97 (and probably much less) to get into Harvard on rare occasions. But just as the AVERAGE height in the NBA is extremely high, so too is the average IQ at Harvard (though not the ridiculously high Nobel prize winner levels that their SATs imply)

LondonYoung said...

The undergraduate program at Columbia has produced 16 Nobel-ish prize winners but Stanford only 2.
Now, this is a pretty narrow and biased metric, but ... 8:1?
So, yeah, I think Columbia produces BETTER graduates than Stanford does.

David said...

Yes, I completely forgot that Caltech's class is only 200, while Harvard's is around 1650.
Lately, Harvard and MIT have gotten the lion's share of IMO contestants from the U.S. Back in the 90's and early 2000's, you saw a decent number go to Princeton, Caltech, Duke. I think college admissions has become even more stratified in recent years, so that a handful of schools are getting a disproportionate amount of the most talented students (mainly Harvard, MIT, Stanford for STEM and Yale for humanities).

David said...

Regarding your last paragraph, I agree that it's harder to quantify management/business skills than pure G-loaded abilities. But having said that, the top b-schools do have a systematic approach towards assessing the combination of skills that will make someone successful in business: work ethic, savvy, strong communication, leadership, teamwork. I know these are all "soft" and "fuzzy" compared to raw intelligence, but consider the following. Most of the people getting into say HBS, Stanford, Wharton, did well at top colleges and then performed well at top banks, hedge funds, private equity firms, consulting, corporate strategy, etc. Aren't such accomplishments good measure of one's management skills? Especially in business, by the time you're in your late 20's, you can tell who's going to be a player and who's not.

steve hsu said...

Rigorous types question whether you can really measure alpha (i.e., true effective alpha not just performance relative to benchmark) even for a pm who has been trading for, say, 5 years. Along similar lines, can you tell the difference between a BS artist who is good at impressing people (i.e., superiors) and someone is actually effective in getting the most out of a team? Can you sniff out a high functioning sociopath? Can you do it using only a paper trail of references (selected by the applicant) and a brief interview? What's the hit rate in the CEO or C-level selection process at most companies?

Iamexpert said...

My cousin credits that the lessons he learned from his MBA program as instrumental in his considerable entrepreneurial success. One man's opinion.

David said...

Well, getting jobs at top firms straight out of undergrad is quite difficult. First, the firms use GPA to weed out those who are not smart and/or unmotivated. Second, the interviews screen for students who are great communicators and cope well under pressure. The consulting interviews in particular also pick out for analytical ability since it's pretty much all case study questions.
Regarding references, in most cases, people are not going to write strong recs unless they genuinely think the person did a great job. And adcom is very good at sniffing out the genuine letters from those that are "fluffed" up. I'm not saying that MBA admissions is a perfect measure of one's business potential, but I think it's pretty darn good at identifying the winners. HBS, for instance, has produced a disproportionate amount of C-level executives at F500 companies, even after adjusting for class size. The difference between HBS and other top b-schools such as say Booth or Kellogg is actually substantial when it comes to producing leaders.

Iamexpert said...

You could make the same arguments about academics or even Nobel prize winners. Many are sociopathic BS artist who repackage and take credit for the ideas of their colleagues.

David Coughlin said...

... management skills (for example) would be much harder to determine from an applicant file.

That made me chuckle because both its understated truth and the corollary deeper truth [that if you have management aptitude, you are better off practicing it, not studying it; so MBAs are for defective would-be managers]

Diogenes said...

good on ya bg2b!

heidegger i do understand most of the time. he's not a faker. hegel is still mostly gibberish to me, but i can tell that hegel is, UN-like late 20th c french "philosophy" trying to make sense, trying to say something. for one thing his vocabulary isn't that large.

kant's ding-an-sich IS a problem. the resolution of it should be almost unintelligible. hegel claimed a solution.

"intelligibility is the death of philosophy"

Diogenes said...

those are all very good points.

if the highest "iq" class were what one wanted it should be determined by multiple tests. the current system has only a few, all of which, like the SB, are very verbal iq heavy. mathematical ability and verbal iq have a large overlap. the math verbal dichotomy is a false one.

Diogenes said...

yes. there is no doubt that elite us unis have a very smart student body, but given the subjectivity and opacity of admission decisions i can't see how this population can't be LESS smart than the corresponding population in other developed countries and even in some developing countries like china and brazil where admissions decisions are transparent and objective, based solely on a test score, i think.

Diogenes said...

ly is forgetting that columbia is in nyc and that nyc has a very different ethnic make-up.

i had a prof of synthetic organic who thought the gen ed requirement was why the us outperformed in nobels. but if it weren't for that very talented ethnic minority i think the us would not outperform.

Diogenes said...

"Obviously, talent in the middle part of the country is not nearly as strong as on the coasts"

only obvious if one is as prejudiced as coastal admissions personnel. these people see arkansas and think red neck. ONLY in america does the "labor party" establishment HATE poor people. to be poor in america is to be evil, hence the lack of class consciousness in america. poor people are ASHAMED of being poor.

Diogenes said...

of course all of this come down to:

those who work for wages and those who work for profit are NOT part of one "labor" market.

part of the proletariat's false consciousness is thinking of the rich as if they were the most skilled, the most useful, etc.

Diogenes said...

as steve said it's a self-fulfilling prophecy.
and of course steve's talk of talents other than intelligence plays into the "there is no such thing as society or class" ideology. that is, very often having people skills and communication skills means de facto you are one of "our kind".

Diogenes said...

"Success in many fields depends as much or more on other factors like intuition, people skills, determination, etc."

and the etc is quite underrated in america where the population has been conditioned to think they live in a meritocracy. but even if there were class-independent criteria, as lapham explains very well, what constitutes merit is determined by the ruling class.

it's not so bad in the us as it was in spain when the visigoths ruled or in ireland when the english ruled where the difference between ruler and ruled was so obvious. it is not so bad as it is and has been in latin america for 500 years. BUT there are class differences whic have more to do with absolute merit than whether on is an Anglican or an RC, speaks quechua or spanish, etc.

one reason why the illusion of meritocracy is actually easier to maintain in a more stratified society is that people of different classes rarely interact except in the most formal way.

for more ;) see the example of Tom Tarter in doctor's diaries.

Diogenes said...

facility with abstractions, even abstractions which are not clearly abstracted from any experience, is a talent in in itself.

heisenberg got it right when he said, iirc, "the reality IS the mathematics."

if one can accept this, there is no difficulty. galileo thought the same way i think.

i had a professor who put it even better, "atoms are perfect." that is, atoms ARE platonic forms, ARE mathematical objects. of course once one sees this he can no longer be a "vulgar materialist".

Kris Roys said...

How many of these Nobel Laureates earned their degree from Columbia in the last 30 years? While it often takes decades for scientific discoveries to establish the track record and esteem necessary for consideration from Nobel Prize committees, how confident are you that the 8:1 trend will continue? For example, do you think Columbia lands as many genius-level East Coast Jews it once did in the first half of the 20th century? Or are those kids going to Harvard and MIT these days?
In terms of recent alums, how many Columbia grads v. Stanford grads are major innovators, execs, mover & shakers in the tech and VC industries? This is nothing against Columbia U. My issue is not with a particular school's spot on the list as it is with the methodology of the ranking as a whole which is wonky at best.

robotizen00 said...

I agree with you to *some* extent. (Came from a middle class, non-professional family.)

That said, there are differences in average talent levels between states. I.e., the National Merit cutoff is ~202 in AR and ~221 in MA. (I think part of this can be explain by the awful school system in AR.)

Around 85% of Arkansans take the ACT, and around 100 score a 34 or above each graduating year. At Wash U, the 75th percentile is a 34. I'm not sure what percentage at Wash U take the ACT, but assuming it's 100% (big assumption), that's around 1600 undergraduates who scored >=34.

oregonlocal said...

That's good news because both Heidegger and Hegel are irrational mysticists who engage in metaphysics which by definition doesn't exist.

Diogenes said...

There, there.
There, there.
There, there, Vivian.
It's a windy day.
Don't worry, dear.
Let's see.
Shall I recite something to you?
Would you like that?
I'll recite something by Donne.
Very well.
Let's see...
"The Runaway Bunny,
by Margaret Wise Brown.
"Pictures by Clement Hurd.
"First Harper Trophy edition,
"Once there was a little bunny
who wanted to run away...
"so he said to his mother,
'I'm running away.'
"'lf you run away,' said his mother...
"'I will run after you.
"'For you are my little bunny.'
"'lf you run after me,'
said the little bunny...
"'I will become a fish in a trout stream...
"'and I will swim away from you.'
"'lf you become a fish in a trout stream,'
said his mother...
"'I will become a fisherman,
and I will fish for you."'
Look at that.
A little allegory of the soul.
Wherever it hides, God will find it.
See, Vivian?
"'lf you become a fisherman,'
said the little bunny...
"'I will be a bird and fly away from you.'
"'lf you become a bird
and fly away from me,' said his mother...
"'I will be a tree
that you come home to."'
Very clever.
"'Shucks,' said the little bunny.
"'I might just as well stay where I am...
"'and be your little bunny.'
"And so he did.
"'Have a carrot,' said the mother bunny."
Time to go.

Iamexpert said...

Foreign universities may emphasize test scores more than American ones, but their tests might be more coach-able and less g loaded than the SAT, so perhaps it's a wash.

Diogenes said...


because even if these were more coachable they are not merely more emphasized, they are the ONLY criterion.

"In a longitudinal English study, g scores measured at age 11 correlated with all the 25 subject tests of the national GCSE
examination taken at age 16. The correlations ranged from .77 for the
mathematics test to .42 for the art test. The correlation between g and a general educational factor computed from the GCSE tests was .81."

it is inescapable. it is simply a statistical certainty, not to mention obvious from experience, that the american elite, though very smart, is chock-a-block with pushy, obedient strivers who are absent from that of other countries elites.

if the sat, act, gre, last, etc. were the ONLY criterion, then the opposite would be the case.

Diogenes said...

i met a grad student in some sort of engineering from nz. he said the gre was the first test of its kind he'd ever had to take.

i think that national level tests in NE Asia and India are comparable, but again the sat, etc. are irrelevant if one's hs is shit or if one doesn't have a 4.0 and 7 extra-curriculars.

it is so obscene that hsers are often aware of this well-rounded bullshit and so seek to make themselves well-rounded. the one guy i went to hs with who got into harvard stared at the floor until he decided he needed something more. he ran and was elected hs president.

if one agrees with soros and popper and the adage that "if you can't measure it, you can't change it" then the opaque, idiosyncratic, and subjective admissions decisions of america's elite schools should be hateful to you. any system which does not allow for its own falsification is a bad system.

when the perfect is made the enemy of the good in these admissions decisions the result is they can never change, can never be criticized.

dwbudd said...

There are three items wrapped up, IMHO.

First, the question about when the products of a Columbia undergraduate curriculum earned their Nobel prizes is important. Was the bulk within the past 10 years? 25? 50? Recall, 50 years ago, Stanford was more or less a regional university where upper middle class parents on the west coast sent their kids for college, because the elite east coast schools were too far.

Second, I think one really should consider the reputations of the graduate vs. undergraduate programmes. Stanford's high profile, again IMHO, arises largely from its graduate schools. These select - and have selected - from elite student pools for many years. Some of the halo over Stanford's intellectual bona fides is due to the greatness of the grad schools, and is not merited by its undergrads. This is changing, but I would say is worth considering.

Finally, Stanford's emergence as a top-tier undergraduate school has been fuelled by the changing demographics in California, I suspect. The general culture on the campus is not strongly intellectual, at least among the undergrads. That is gradually changing.

Given time, I would suspect that Stanford will overtake Columbia.

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