## Monday, March 13, 2006

### IQ in different fields

Steve Hsu has found a very interesting table with the average GRE scores computed for various concentrations. He has also defined a linear map translating the average V-Q-A scores into a more familiar IQ scale. This convention looks natural to me and I will follow his scale although it is not guaranteed that it is equally calibrated as other IQ measurements.

Disclaimer: these cold numbers expressing typical IQ for different occupations must be interpreted very carefully. They don't necessarily imply anything. The outcome depends on the character of the question, discrimination, etc. Despite different numbers, all of us are equal. Blah blah blah. And so on.

The results are:
• 130.0 Physics
• 129.0 Mathematics
• 128.5 Computer Science
• 128.0 Economics
• 127.5 Chemical engineering
• 127.0 Material science
• 126.0 Electrical engineering
• 125.5 Mechanical engineering
• 125.0 Philosophy
• 124.0 Chemistry
• 123.0 Earth sciences
• 122.0 Industrial engineering
• 122.0 Civil engineering
• 121.5 Biology
• 120.1 English/literature
• 120.0 Religion/theology
• 119.8 Political science
• 119.7 History
• 118.0 Art history
• 117.7 Anthropology/archeology
• 116.5 Architecture
• 115.0 Sociology
• 114.0 Psychology
• 114.0 Medicine
• 112.0 Communication
• 109.0 Education

If you trust these numbers, one of the conclusions is that the economists are the brightest among the social scientists (rank 4) who are only followed by philosophers (rank 9). The philosophers are still brighter than political scientists (rank 17) who are smarter than the sociologists (rank 23). This list may confirm virtually all of your preconceptions about all these fields, at least it was my case. The only exception was medicine that I expected to appear in the upper half.

Let me remind the dear reader that the IQ is normalized in such a way that all the people in the world are distributed along a Gaussian (normal) distribution with the mean value IQ=100 and the standard deviation ΔIQ=15. So 34.1% of the people should be between 85 and 100, 34.1% of them should be between 100 and 115, while e.g. only 2.5% of the folks should be above 130, including those 0.15% of folks above 145, and 2.5% of them should be below 70, including 0.15% of folks below 55: the latter groups are called, in the technical terminology, morons, idiots, and imbeciles.

You may also want to study the table of average IQs in individual nations. As a Czech – a guy from a nation whose average IQ is just 98 – I may still use my personal IQ of 187 to safely predict that you are Japanese, i.e. a member of one of the 5 smartest nations whose average IQ is 105, and even play Kimigayo for you. ;-)

There is a whole IQ category on this blog with 30 articles which are dedicated to intelligence, especially the IQ differences between the two sexes.

The IQ of a field seems to be slightly negatively correlated with its hotness. Click the graph for a source with some extra information.

1. Dear Luboš,

re: In "IQ in different fields" you made the following statement: "The only exception was medicine that I expected to appear in the upper half ( of the list of Mean IQs )." Average IQ was 114 for medicine fourth from the bottom only Communication, Education and Public administration were lower.

I am a physician and entered medical school ( Ivy League ) in the early 1960s. At the time I took the GREs ( score 960 in Biology out of 970 top score and 800 verbal, and 800 math ). The stellar GREs did not help me get into Medical school because I already had been accepted before taking the GREs during my 2nd semester of my last year of college. There was no GRE exam for Medicine then or now to my knowledge. Prospective medical students in the 60s took the Medical Aptitude Test some time before applying to medical school and that still is being done as far as I know. The Medical Aptitude Test has been dumbed done since I took it as have the SAT exams. The Medical Aptitude Test was a darn hard test at that time. During my time in medical school ( 1960s ) and the year after I graduated, there were three tests given nationally to medical students ( and I suspect currently ): 1) at the end of the second year, a basic science exam, 2) at the end of the fourth year, a clinical science exam, and 3) at the end of one's Internship ( or equivalent 1st year residency ), an applied clinical science exam. No exact grades were reported back to the student, only one's percentile rank which made a great difference later in getting into a top residency program and was used to get a medical license to practice medicine in most States of the USA.

My hunch is that the Medicine GRE must be in reference to Nursing, Audiology and possibly Physical Therapy not true MD students.

Check out this URL http://members.shaw.ca/delajara/GREIQ.html .

Here is Rodrigo de la Jara's information on "How to estimate your IQ based on your GRE or SAT scores." Linked on that page is http://members.shaw.ca/delajara/Occupations.html "Modern IQ ranges for various occupations." The MDs were the brightest on average of occupations but Natural Science included physical, life and math. There is much to mine relating to IQ on de la Jara's site.

Now another topic. A nephew of mine who has been followed by the John's Hopkins High IQ study as he grew up, did not get into Harvard's on coming Freshman class; he is on the waiting list but will never attend if eventually accepted. He will attend Colgate University and it will be Harvard's loss IMHO. His SATs were 800 verbal, 800 math, and A+ Essay. He knows of two females and two blacks with much lower SATs who were accepted to Harvard and who have no where near his Academic and Extracurricular achievements such as being High School Newspaper Editor his Junior year--it was a competitive position not restricted to Seniors. This perceived insult by Harvard will bother him for years because of its injustice. I urge you to read the following essay: Down, Down, Down--Reflections On The Boy Crisis http://fredoneverything.net/FOE_Frame_Column.htm .

Cheers,

Atlantin

2. Hmmm, I don't trust these numbers. I looked at the ETS stats for the GRE and according to my calculations, physics are #1 but philosophy is #2 and mathematics comes in at #3.

I think Hsu's #s are from added scaled scores from the three subtests. Wouldn't it be more accurate to get the deviational scores since the three subtests of the GRE have different averages and SDs? Simply adding the 3 subtests would give the quantitatively strong disciplines a decided advantage on the rankings because the average scaled score for the quantitatuve section is much higher than it it is for the verbal. The verbal section also have a much smaller SD.

Philosophy majors have the highest verbal scores, the second highest quantitative scores for humanities-social sciences majors (just behind economic majors) and the 3rd highest analytical scores overall behind physics and math majors.

On the newer GRE test with the analytical writing section, philosophy majors have the highest overall deviational GRE score of any major. This subsection gives phil majors an advantage and so probably should not be included in rankings. From just the verbal and quantitative sections, phil majors are still right behind physics majors.

3. Dear Chevo, trust whatever you want but these numbers are directly taken from this page. Philosophy is at rank 9, with 585,597,621 in V,Q,A GRE tests. I didn't invent the ranks, just translated them to expected IQs. Best, Lubos

4. I'm amused to see lawyers don't appear on the table. Presumably their IQ's are too high for the scale ;>

5. I suspect the engineers have their scaled scores biased downward due to their verbal skills. I know a few engineers with fantastic analytical/quantitative skills, but are lacking (somewhat) in written communication...

6. heh, that's true,i dont know where this data is coming from (frankly, i only want to prove you wrong, heh). The guy probably lumped all healthcare professionals, from medical assistants to doctors, into one category. I trust this paper more: http://www.ssc.wisc.edu/cde/cdewp/98-07.pdf (pay attention to figs 8, 10, 12)

7. Enjoyed reading through comments and your post and found it very interesting. I was rather amused by all the comments from md's trying to convince themselves they had to be higher in ranking though they seem to be rather logical. Dr's must do very well in school and pre-med in a broad spectrum of mostly mundane studies. They learn and are great note takers and excellent at studying and repeating what they are taught. There's little or no room for deviating from the norms of what is known and expected. You would not expect someone who had a lot of insight to be that much of an automaton. All said professional schools are not created for the highly gifted with all their positive and negative qualities if you choose to refer to very high IQ's as gifted.

8. I often notice that a lot of people completely overlook one pretty obvious reason, why students of certain disciplines, escpecially those called "hard sciences", often land at the top at those standardized tests on average: Students of Economics, Physics, Computer Science etc. are more or less "training" for the math part of the GRE everyday, just by doing their daily learning. What is required for the math part is basically their "bread an butter", to advance in their field they have to train the math to succeed. Most of the social sciences, except for economics, just require you to leanr the basics of statistics. So it's really not a surprise that certain fields do better than others and that doesn't necessarily has anything to do with their IQ (btw, it's just a psychometric test, and is in fact changeable -> neuroplasticity). It would be interesting to investigate if students of certain fields do different at certain standardized tests like the GRE Math part before and after their undergraduate studies. Of course you have to take things like graduation rate into account. I am convinced that you will see a certain divergence of the Math score when you compare social vs. Hard sciences which would be partly due to the fact of training. So what about the Verbal Score? I think that just those studying English or languages will benefit from their studies. And by the way, psychologists have found that your scope of vocabulary is the best proxy of your "intelligence" or "IQ" (which, keep in mind, is changeable after all).

Kind regards and many greetings from Berlin, Germany
Sebastian

9. Hmmm. I see that

FindRoot[Probability[x>=iq,x$Distributed]NormalDistribution[100,15]]==1/CountryData["UnitedStates", "Population"],{iq,150,100,200}] gives {iq -> 187.059} 10. Dear Steve, excellent calculation. Most of other people know the number 187 as the IQ of Sheldon Cooper but it was cleverly chosen to emulate a plausible IQ by the smartest American. Cheers LM 11. With an IQ of 187, Sheldon would handily qualify for membership not only in Mensa but also the Prometheus and even Mega Societies. But what of people possessing even greater IQs? Supposedly the scale breaks down once you get past Sheldon's 187 and break the 200 points mark. This is actually not true as I show below: If  \left(\sum_{k=1}^n a_k b_k \right)^2  then  \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } }$\$

and then by simple chromularinversion we find that all IQ > 200 wrap around the back and then continue, starting from n=1, a phenomenon known as Doubly Speshul Intelligence (DSI), which means --

What's that? Gibberish? Ah yes, dear Lubos, you would say that of course, as the benighted possessor of a singly special intelligence.

Well, don't trouble yourself too much and go back to playing with your twistors. In the meantime I will solve cancer and the P ≠ NP problem. Should be done by dinnertime tomorrow.

Signed, Eugene S
IQ 74 [DSI]
Member, DENSA (Doublyspeshul Education-Negative Slacker's Association)
P.S.: I have a simple C++ program that interactively demonstrates the above concept but the margin of this comment box is too narrow to hold all eight pages of it.

12. What's the SD for Czech Republic if your IQ is 187 and the average is 98? How it could it be 15? Seems more like 50...

Does that mean there are only like 10 people in Czech Republic with an IQ above 172?

13. Dear itsnobody, let's remote the personal dimension from this question.

Now, when it's removed, I must say that your reasoning is statistically faulty because it doesn't take the so-called look-elsewhere effect into account. If you find a subgroup - nation in this case - which contains an element with unreasonably extreme characteristics, it does not mean that you have demonstrated a contradiction or implausibility of the parameters of the distribution because there may exist many other subgroups that don't contain such an extreme element.

So it makes no sense to constrain your attention to the Czech Republic unless you have information about the IQ-187 people in other, comparable nations.

Just try an extreme version of your "localization" to see why it's wrong. In this apartment house, there may be 50 people, so even a person at IQ=145 is "almost impossible" to be found here - at a 90% confidence level or so. That doesn't mean that there's no person with IQ=145 or greater here.

14. You didn't really answer the question, what's the SD for Czech Republic? Do you know what it is?

I didn't argue a contradiction, I simply asked if that would mean that there are only around 10 people in Czech Republic with IQs above 172 since Czech Republic's total population size is 10,546,000.

Your apartment house analogy is flawed because it doesn't take into account the average IQ of the 50 people in the apartment house.

A better analogy would be 50 people in an apartment house, the average IQ is 98, and 1 of them has an IQ of 145, what's the SD within this sample of 50 people?

The SD for each nation cannot obviously be the same.

For those who don't understand how important knowing what the Standard Deviation is consider this:

An average IQ of 105 with an SD of 3 would mean there would be virtually no genius IQ people in this group (but the average IQ appears high)

An average IQ of 97 with an SD of 50 would mean there would be lots of geniuses within this group (even though the average is lower)

The Standard Deviation tells us how much variation there is from the average value.

So an average value without the SD wouldn't tell you much if you were trying to find out the percentage of geniuses in the group.

As for East Asians, their population size is above 1500 million, their average IQ is also high, but I don't know what the SD for their group is.

Some other questions:
- What type of IQ tests are used, are they all very similar in type all around the world (if not this would give inaccurate data)?
- What's the sampling error and standard deviation?

It's just like the saying goes "lies, damned lies, and statistics"

15. Dear its nobody,

the IQ standard deviation in the Czech Republic is 12 IQ points, so the Czech nation is clearly more egalitarian than the mankind whose standard deviation is by definition 15. 187 is formally 7.42 standard deviations above the average IQ of 98.

But that's an irrelevant information for the questions about the tails because once we admit that Czechia's IQ distribution deviates from the global distribution, we must also admit that it deviates from any normal distribution, so you can't calculate the probabilities just from the mean value and the standard deviation.

Even if you could and a person with IQ at 187 would turn out to be very unlikely, it doesn't mean that it's impossible. The Czech Republic could have been very well "cherry-picked" as the country that just happens to harbor a person with the IQ equal at 187. A convincing "proof" that something doesn't seem right could only be obtained if you took the most inclusive population you may get - the whole mankind - and you would still calculate that the probability is insanely low. That would be an argument for the assertion that some of the assumptions are flawed.

Your comments about the calculation of apartments are clearly complete bogus - that's the fallacy I mentioned above that you brought into ad absurdum dimensions, except that you apparently think that your reasoning is valid.

If there is an apartment with 2 or 5 or even 10 people, it's clear that the number of folks in the apartment with IQ above some high value can't be accurately obtained just from some mean value and the standard deviation because the distribution obtained from 2, 5, or 10 people is highly non-Gaussian - it's the sum of 2, 5, or 10 delta-functions, in fact.

Cheers

LM

16. One big problem- doctors didn't take the GRE, they took the MCAT. So who's taking the GRE in medicine? Answer: slackers who couldn't do well enough on the MCAT to make it into a med school and are looking at lesser positions in nursing, physical therapy, lab technicians, etc.

17. To say that the Czech Republic has a different standard deviation than the one used, globally, for IQ norming, is illogical and I believe expresses, on your behalf, a lack of understanding of the psychometrics involved.

The standard deviation, like the mean, is arbitrary. It is defined to be 15. That is a normalization constant. If you are making the claim that your IQ is 187 on a s.d.=12/mean=100 scale, then you are claiming that your IQ is based on a sample from another planet where the population is roughly 50 times that of Earth's.

If you were to modify your claim to the statement that your IQ was 187 on a s.d.=15/mean=100 scale, then you are still making the claim that you are among the dozen or so highest IQs on the planet, which is absurd because it carries with it the implication that the test(s) involved have covered enough cases across a wide enough range to be statistically valid at the +/- 6 s.d. threshold.

I don't doubt your IQ based on the way you speak, though someone less knowledgeable on these matters would most likely immediately come to the conclusion that based on your flawed, illogical, and inefficient use of language, your IQ couldn't possibly be that high.

No. I doubt it on the basis of its statistical unlikelihood.

Others might dispute your claim on the basis of your failure to understand the statistics of a concept as simple as a standard deviation. And they would have a stronger argument than those pointing out your childish grasp of language. Yet still, it would not be a strong enough argument to disprove your claim outright.

But actually, the unlikeliness of it being true is enough.

The standard deviation for IQ is defined to be 15 but it's the standard deviation for the mankind. Within groups that are less variable and whose members are more alike, the standard deviation will obviously be smaller.

For example, among women, the standard deviation is about 10% smaller for IQ. This is actually by far the main reason for the women's underrepresentation in elite mathematics and related fields. By your confusion about these basic facts, you look like you have just fell from another galaxy.

19. The Ultimate PhilosopherSep 20, 2013, 1:38:00 AM

The usual division is into the physical sciences, the social sciences, and the humanities. Philosophers come out on top in the last third (of course).

20. I believe that the medicine/IQ association provided here is misleading as it may appear to be in reference to medical doctors. It probably not only includes medical doctors but also individuals in medical-related fields. The mean IQ of medical doctors is about 125 if I am not mistaken.

21. The number of 125 provided above for medical doctors is under the assumption of population sd of 16, not 15 (it was an old study).

22. Philosophers are pretty smart for not being mathematically literate.

23. Smack Dat Class GurlMar 2, 2014, 10:51:00 PM

I knew my iq was higher than 102. I am flying through biology with no problems understanding nature's basic yet processes (so far). Other students complained it was too hard lol. Turns out I am twice exceptional and my IQ cannot be quantified accurately at least by that particular iq test. So I am probably at least 120 to 130 ( according to psycologists). Hooray!

24. That doesn't mean you have an IQ higher than 102.

25. Oh...my...god. Another guy on the internet one upping himself from the general population with benign and linear banter that reveals in and of itself the bitter grayness of incompetence. You primitive little insect, was the world unfair to you? Are you that far gone that you must attempt to fend us off with the blunt club of faulty analysis? I hope not. For as long as you struggle, the farther you are distanced from yourself courtesy of your feisty little ego. Tsk tsk tsk. Find a hobby. Join us. We don't bite. Embrace promises your emotional insurance not be taxed, and our wants not be leached. You are more than this. Leave your computer, and prove it. We all love you.

26. IQ is a funny thing. Just because you have a higher than average intelligence, doesn't mean you pick a hard major. I have a friend who is smart who went into accounting, as he liked numbers but didn't want a hard occupation. He could have been a doctor, lawyer, engineer, or mathematician, but chose accounting. I knew engineering students in school who went into actuarial sciences and physical sciences (chemistry, etc) due to desire.

For me I chose engineering. I was one of the gifted ones in electrical engineering, and was in the top 3 in my class. I too, could have chosen any field based on my aptitude. I chose engineering due to maximum pay for a 4 year degree at an in-state school. I didn't desire medical due to my lack of interest in learning archaic terms for medical minutia. I also wanted to be done in 4 years, so lawyer was out.

I read the article, and know as a fact that IQ varies on 5-7 metrics, with few who are able to max out on all. People who are logical often lack communication skills. People who are socially skilled and have great bedside manor can't do the memorization and recall required to be a doctor. Street con artists have IQ's for social and personal skills that are rivaled by social climbers and politicians, but are difficult to measure by a test.

In the end, you rarely get a car mechanic, surgeon, lawyer, doctor, engineer, social butterfly, counselor/physicist. Why is due to forced differentiation by society and schools. it would take a lifetime to learn all things and master all things, but it has maximum reward to pick something that you find rewarding, then use it to make your way in life.

IQ is meaningless if you aren't happy. for that reason, geniuses will be teachers at just above minimum wage, and the not-so-smart who are pretty and witty will climb social ladders and be managers and politicians. some will choose power, others wealth, others happiness.