If you are not too stupid you can be in Mensa

By Razib Khan | April 17, 2012 5:30 am

Is 4-Year-Old as Smart as Einstein? Not Quite, Scientists Say:

One of the latest members of the high-IQ club Mensa is a mere 4 years old, with an IQ of 159 — but psychologists warn against pulling out the Albert Einstein comparisons just yet.

“All you’re doing with IQ testing is testing within a certain age group,” Lawlis told LiveScience, explaining, “You’re saying the 4-year-old is smarter than 99.5 or 99.8 of [her] age group, but that doesn’t mean you can compare to another age group.”

I’m a little confused here. It seems to me that the biggest issue with IQ tests given to very young individuals is expected variance in outcomes across tests. Raise your hand if you know a moderately bright person who “tested off the charts” as a very young person. If the charts are such that people test “off them,” I am skeptical of the precision of the tests being used.* My own hunch when someone tells me their IQ is that if they are moderately gifted they are reporting from the high range of distribution of scores they’ve received. Many gifted children have taken a fair number of standardized tests, so it isn’t too difficult to sample from the higher of the range of outcomes. 90 percent of people think they are better looking than average, and 90 percent of people report they are more intelligent than average. Why should we credit the cognitively gifted set with much greater self-awareness of the usually unconscious bias of overly positive self-assessment? (yes, I know of the Dunning–Kruger effect) If someone took the SAT three times, do you think they’ll be reporting the average of their outcomes, or the best of their outcomes (probably the last time they took it)?

Which gets to my title: from what I recall Mensa allows you to keep taking IQ tests as long as you want (you may have switch tests though, but that’s not too hard, there are plenty of them out there to select from). If you are within spitting range of the top 2 percent you will eventually cross the threshold simply by taking enough tests because the results are somewhat noisy. An individual whose average score is in the 5th percentile across tests may still find a test which allows them to break the 2nd percentile floor for Mensa. I suspect that measurement error of this sort is at the heart of Richard Feynman’s legendary “low IQ” by the way. He was smart. He had to take lots of tests.

* Personal story, when a friend told me at one point that they’d been tested at a 150 IQ when they were young, I unwisely replied that it was obviously measurement error, and their real IQ was probably closer to 140. I knew their SAT test scores, and I also knew the person well enough to gauge their intellect. My friend did not press the point after I told him baldly that he was surely reporting his highest score. But I don’t recommend this course of action to people who are interested in maintaining friendships. A many an ego has rested uncomfortably within the house which measurement error has built.

MORE ABOUT: SAT, standardized tests
  • Eurologist

    Interesting (self-) discussion about how to communicate the difference between test scores and personal assessments.

    Scientifically, I have no idea how early-childhood test-scores translate to success or academic success later in live. Personally, I wager there is a high correlation.

    Anecdotally, I seriously had no idea how high I would test until I was close to my PhD and friends invited me to do so, at about 2-3am and many bottles of wine, later— and that pattern repeated, several times over the past decades.

    Coming back to the original story, of course, much detail is missing. But — I also learned how to read before formal schooling (I kept asking family members if certain advertisement signs and newspaper headlines meant what I thought they did, and at the same time learned numbers by playing cards at age 4-5). I had a great teacher in the first 4 years of school, and I always was the last-person-standing in the first few grades’ math contests where anyone not keeping up had to sit down in a long series of simple math tasks (such as: 2 times 6 minus 10 times ten minus ten times 2 divided by 5 times 8 minus 3.., etc…) – even though simple memorization was my single-worst topic.

  • http://blogs.discovermagazine.com/gnxp Razib Khan

    just a minor note: not too interested in personal stories of how you found out you are smart. i know plenty of smart people, and i trust most of the readers of this weblog are smart. hope that’s clear enough for people in the left half of the social intelligence curve.

  • Karl Zimmerman

    My IQ defiantly did fall back a bit from childhood to adulthood. When I was young, it tested at 135, but as an adult it’s come out around 129. Mind you, I also have some learning disabilities associated with ADHD, which hurt a few subsections, plus math score comes in pretty low, at 104, so other portions test around 140-150.

    More apropos, however, is my wife. Her parents claim that her IQ as a child tested around 160-170 (they can’t remember out of their two children who scored higher). While she is undoubtedly smart, I have a hard time believing she is significantly smarter than I am, as typically I figure out things before she does, and have to explain something to her 2-3 times sometimes.

    However, much of that may be due to her personality, and first career as an engineer (although she is now an architect). Even she has noted that although engineers are typically bright but uncreative and single minded. She certainly doesn’t show interest in a broad array of intellectual subjects like I do, and she seldom wants to tackle a problem until she’s read extensively the “by the book” ways to address it.

  • pconroy

    When asked my IQ I reply 157, as that’s my highest result, but I’ve tested:
    135, 143, 145, 148, 157

    I view it like sprinting, you always give your best time/performance result?!

    What type of engineering are you referring to when you say engineers are uncreative??

  • Karl Zimmerman

    pconroy –

    My wife’s undergraduate background was in structural/civil engineering. Before she returned to graduate school, she worked in MSHA, where I believe much of her job was examining the causes of mine accidents and fatalities.

  • jb

    I think you can do real harm to children by telling them how smart they are. My mother was deeply invested in the idea that her son was a little genius, and talked about it constantly — especially to me! In particular I seem to have scored above 170 on an IQ test some time before second grade, so that was my IQ, period. I am in fact reasonably intelligent (e.g., 99th percentile on both the math and verbal SATs), but growing up thinking of myself as a genius, before I had actually accomplished anything in life, gave me a very wrong idea of what life was about, and in retrospect I see that it was quite bad for me. I would have been better off, and very likely would have accomplished more, if the subject had never even been brought up.

  • miko

    My IQ was tested when I was around 10 — I was enrolled in a clinical study. My parents have never told me what it was, and I’ve never really been tempted to take an IQ test. I mean, is it that hard to kinda figure out where you are on the intelligence spectrum just through living your life? I’d be curious why people want to know their score on an IQ test.

  • http://blogs.discovermagazine.com/gnxp Razib Khan

    I’d be curious why people want to know their score on an IQ test.

    inverse-feynman. if you underachieve it is a good source of self-validation.

  • miko

    I can see that… being a 2nd/middle child I could never take grades and performance rewards all that seriously (though I cried when I came in last in the Pinewood Derby — my vehicle was overdesigned), while my oldest sib won every possible academic thing there is. When I took the SAT, I was like, see mom and dad… my great scores will get me into a college you want me to go to, never mind my grade under-performance and attendance problems. Then a guidance counselor told me that in the minds of admissions committees: great test scores + great essay + so-so grades = lazy. I can thank the geographical box-ticking of east coast liberal arts college admissions offices — they think students from flyover states are diversity.

  • AG

    My IQ test is moderate good. But my tests on SAT, GRE, USMLE, are at 97-99 percentile.

  • http://blogs.discovermagazine.com/gnxp Razib Khan

    #9, aptitude X conscientiousness = school performance. correlation is imperfect :-)

  • pconroy


    As a kid I went to a 2 room primary school, and my teacher told my mother numerous times that I was “slow”, and should be held back a year. This was even though I had taught myself to read at 4 yo, and had read all the books in the school library (about 40 outdated books total) years before I finished primary school. Eventually my mother was convinced, and held me back a year before high school…

    So knowing that this was incorrect, is somewhat validating… 😉

  • Polynices

    The three IQ tests I’ve taken (each ten years apart, as it happens) were reported as a small range of values, not a single number. That seems like a better way to do it given the expected variance in outcomes across tests as you say. Maybe my experience was unusual in that I was given my scores in a sensible fashion?

  • Violet

    I think children have a large variability in development along different dimensions. My son started reading at 2.5years and reads all landmarks in a 30min drive through the city. He can write simple words, do simple addition and read at grade 1 level at 3.
    But I don’t think him as a genius because he is developmentally slightly behind the average in social awareness, and emotional control for his age group. It takes well-rounded or at least average achievement in other dimensions to move forward.

    #5, In defense of structural/civil engineers, ‘creativity’ is defined differently for architects and engineers (ref. Eiffel tower). Architects like to think they are creating functional art form. Engineers are interested in life safety. They are blamed for being too creative even if one thing goes wrong over 50 years (Leslie Robertson-WTC). General public has very low (probability of failure < 10^-5) tolerance for structure collapses. It takes 10-15yrs in the field to be confident enough for creative designs.

    A comment from medical doctor in an engineering seminar is notable, she said, " we think it's a success even if one life is saved. You guys think it is a failure even if one life is lost in an extreme event".

  • http://emilkirkegaard.com Emil

    On the subject of testing and avoiding sample bias. Does anyone know how to obtain a proper broad test somewhere on the internet for free? I’ve been testing my friends with a APM but since it is a verbal test, some people are likely to be misrepresented by this score. I have access to journals, if the test is in a published paper.

  • Anthony

    Aside from early childhood IQs being less correlated with adult IQs than simple measurement variability would suggest, there’s also the problem of incommensurability of scales. Childhood IQs are (were?) calculated as “mental age/physical age”, measured to the nearest month. The number of 8-year-olds who measure out as 11 y 7.2 mo (IQ=145) is greater than the number one would expect to be +3 sigma.

    For IQs of 100 or higher calculated as a mental/physical age ratio, there’s an attempt at providing adjustments (based on SD=16, not 15) at http://hiqnews.megafoundation.org/John_Scoville_Paper.htm

  • http://www.gwern.net gwern
  • Spike Gomes

    I like to do the Feynman thing and cite my lowest IQ score (111 on an unofficial Raven’s test online). Then people can say “But you seem smart” and I can quip in return “Smart-assed!”

    I don’t place too much worth in my own individual score since I know what my limits are intellectually without placing numbers on it, that said, I tend to have more fun when I’m the stupidest guy in the room than when I’m the smartest, so as much as possible, I try to follow Weird Al’s dictum and “Dare to be Stupid” in the face of all evidence to the contrary.

  • KT

    “My IQ test is moderate good. But my tests on SAT, GRE, USMLE, are at 97-99 percentile.”

    Similar situation here. My IQ has ranged between 115 and 122 over multiple online tests that I’ve taken. However, I scored in the 99th percentile on the SAT, GRE*, and GMAT (single attempts, but I prepped the f*** out of these tests). Could it be the lack of a visuo-spatial component on the SAT, GRE, and GMAT? Any other hypotheses?

    I can’t decide whether or not I’m smart :)

    * There’s no cumulative score to percentile conversion for GRE, but my individual section percentiles guarantee that I’m in the 99th percentile on a cumulative basis too.

  • Pincher Martin


    “The three IQ tests I’ve taken (each ten years apart, as it happens) were reported as a small range of values, not a single number. That seems like a better way to do it given the expected variance in outcomes across tests as you say. Maybe my experience was unusual in that I was given my scores in a sensible fashion?”

    Assuming the values reported weren’t for subtests, I’m not sure why a “small range” for a single IQ test should be preferred over a precise score.

    It seems to me that if you want to know how well you did on a test relative to others who took it, you should prefer the precise score. But you also shouldn’t infer from that score that a single test can fix your IQ. It could be a bad test with a low g-load. Or you could have had a bad day. But the best way to discover that would be to take more tests, not assign a range for a good test.

  • Eurologist

    I think children have a large variability in development along different dimensions.

    Of course. My son has a couple of fairly obvious and significant disabilities, but otherwise scores in the 95th or higher percentile on almost all tests. I am confident he’ll find his area where he can succeed – but so far, I have no clue where this will be.

    not too interested in personal stories…
    Razib, proven by the responses, human nature appears to make your goal somewhat futile. Also, personal stories about how people with high IQ view(ed) themselves as children and whether they fared well later in live may be illuminating, as long as we have limited (in more than one way) scientific studies on this subject.

  • AndrewV

    “hope that’s clear enough for people in the left half of the social intelligence curve.”

    Sometimes you hope in vain?

  • Ed

    Scored 118 then 122 on some unofficial test with mostly matrix reasoning and number sequence questions.

  • Syon

    Closest I’ve come to an IQ test is the GRE. My GRE verbal score was 730 (98 percentile). According to La Carrefour de la Sagesse, that’s supposed to work out to an IQ of 140. Anyone know how accurate that estimate is?

  • Dan in Euroland

    Ultimately IQ scores are irrelevant. The only thing that matters is what you produce, and being a decent person to your fellow humans.

    Stop the navel gazing people, and get to work.

  • https://www.facebook.com/mensa.at librarymistress

    we did a IQ test in school – our maths teacher wanted to show how silly (he thinks) we were. We were about fifteen years old then. I really was convinced that all of my friends would have reached a score of 130 (which means the upper 2% at the scale of this test) as I did. But when I mentioned this, there was embarrassed silence all around me. That was the first time I really realised being different 😉 (what didn’t mean I believed in me being superior).

  • Sandgroper

    Well said, Violet.

  • AG

    A comment from medical doctor in an engineering seminar is notable, she said, ” we think it’s a success even if one life is saved. You guys think it is a failure even if one life is lost in an extreme event”.

    At end, medical doctors always lose since we all die. The game of medicine is delaying the inevitable.

  • AG

    Some reality check.


    A lot of readers here have their IQ at least 3 stds above for their respective occupations. Great respect for people choose to do so. You guys make those occupations better than others can.

  • Sandgroper

    AG, we’re both about the same thing – prevention or avoidance of premature loss of life.

    When I was a first year engineering student, my doctor said “You guys matter a lot more than we do. If we make a mistake, we kill one person. If you make a mistake, you can kill hundreds.”

    Not really a fair observation, though – both medicine and engineering are about a lot more than just not making mistakes.

  • Sandgroper

    I still haven’t got Karl’s point about how engineers are not creative, given that engineering is all about creating solutions to problems. But as it seems like he was just opinionating, I’ll maybe let it slide. Perhaps he’s getting confused with technicians, who just repetitively apply known solutions – a lot of technicians call themselves engineers.

  • pconroy


    I think Karl’s error is that he equates creativity with something specific like graphic design or writing or something.

    Where I work, there is a dept labelled “Creative Dept”, that is stocked with such people, yet I dare say that people in my dept are actually the more “creative”…

  • Karl Zimmerman

    No, I know what creativity can mean, and I understand how engineering can involve creative solutions. While I’m not mechanically inclined in the slightest, I do understand that the vast majority of invention is engineering.

    But as I said, I’m going by what my wife has told me. Her father was a mechanical engineer who worked for GM, among other places. He’s now semi-retired, and works as an expert witness for car insurance companies on accidents (velocities, angles of impact, etc. She got her undergraduate degree in engineering, and mostly socialized with engineers. Her best friend, longest-term ex-boyfriend, and many other acquaintances either are current or former engineers. And in her new career as an architect, she works with engineers on a regular basis. She feels like she has enough of a background in engineering that she can provide stereotypes for each kind (mechanical, electrical, chemical, civil, etc).

    She has not gone into great detail about what being an engineer actually entailed (besides it being highly-paid, but boring), but from what I gather, at least within her area, it was reading a lot of code and regulations, and applying equations repeatedly. Within her current job, it seems like the architects to the designing, and then the engineer comes back with a response on all the ways the building may fail from a structural or other standpoint.

    Edit: I think she’s said, broadly speaking, there are two kinds of engineers:

    1. The nerds who like to make things.

    2. The people who need a profession, are good at math, so just kinda end up doing it.

  • floodmouse

    Razib Khan said: “I’d be curious why people want to know their score on an IQ test.” – Answer: Because when I was a kid, I could never win at arm wrestling. 😉

    Spike Gomes said: ” I tend to have more fun when I’m the stupidest guy in the room . . . ” – Reply: I myself may not be the stupidest person ever to post on the Discover blog threads, but I probably have the least scientific training. (Liberal arts major.) The problem is, I never could stand listening to English majors, but I like hearing what the science people have to say.

  • http://blogs.discovermagazine.com/gnxp Razib Khan

    Razib Khan said: “I’d be curious why people want to know their score on an IQ test.” – Answer: Because when I was a kid, I could never win at arm wrestling.

    that was miko, not me.

  • Sandgroper

    That’s pretty much what I am saying. “…reading a lot of code and regulations, and applying equations repeatedly” – yes, that’s working at technician level. Sub-professional. Or not even that.

    That explains everything.

  • Eurologist

    I have tutored a number of engineers, and I have graded mathematical physics classes for engineers many moons ago. From that, I can tell you that a large fraction of engineers are not really mathematically inclined compared to average high-school students (e.g., in the better regions of the US or Europe), and don’t have the drive or capability to employ creative skills to compensate. But, yes, clearly – the top something percentage of mathematical engineers are way up there in terms of mathematical ability and general creativity.

  • Sandgroper

    I have interviewed literally hundreds of engineers for professional qualification and employment, and have worked with hundreds more, and I’m willing to bet I know more about it than you do.

  • Sandgroper

    I am fully familiar with the data on mean IQ of physics vs engineering vs whatever. Frankly, it would be a better world if the average engineering graduate was a bit smarter, but there you go.

    A point that a lot of people don’t seem to get is that there is a difference between someone who graduates with a first degree in engineering, and a professionally qualified practising engineer. If you don’t get the point that one of the things that distinguishes the professional engineer from the sub-professional is the novel element, then you don’t.

    Another point is that practising engineers actually do more than just sit around all day doing calculations or navel gazing. Given that you have clean water to drink, roads to drive on and a sewerage system to shit into, I would have thought that might be obvious to you, even if you don’t actually get the more dramatic bits because you really don’t have much of a clue about what engineers do.

  • Violet

    @Sandgroper, thanks for #27 & #39.
    I think the calculations are the easy part. :)

  • Young Money

    Just out of curiosity, Razib, what was your friend’s SAT score? How could you be so sure that his SATs/your judgement of him indicated a 140 IQ vs 150? I could see how a 2000 SAT would invalidate a 150 IQ claim, but a 2250 SAT wouldn’t necessarily.

  • http://blogs.discovermagazine.com/gnxp Razib Khan

    #41, prerecentered sat was 1300ish from what i recall.

    How could you be so sure that his SATs/your judgement of him indicated a 140 IQ vs 150? I could see how a 2000 SAT would invalidate a 150 IQ claim, but a 2250 SAT wouldn’t necessarily.

    because 150 people are often noticeably smarter than 140 people. 150 IQ is 1 out of 1,000. 140 is 1 out of 150. 140 is commonish in my social circle. 150 is not as common.

  • Violet

    # 42 Razib,

    In your opinion, what would be the criteria for being noticeably smarter?

    Some people could be really smart at getting into the depth of something complex and some can be very quick at catching new idea/theory. Some are better at articulating their understanding and with others you would have to look at their work to know. How do you judge?

    I used to think it would be blindingly obvious when someone is brilliant (like 1 in 1000), but I am not sure anymore.

  • Sandgroper

    Yeah, sounds about right.

    When I enrolled in engineering, the advice from the university was you needed 135 to get through. They didn’t get a mean of 135 in the intake, of course. 50% of my intake failed first year and got kicked out – some due to that, some just due to excessive beer consumption, I think. About 15% of my intake made it through the 4 years without at least having to repeat a year – 10% civils and the others split 50-50 electrical and mechanical. Of those, I’d estimate about half or so are still working in engineering. The first year intake was 196 students, which generated about 15 – 20 people still working in engineering or related management 40 years later, including the first girl to ever graduate from that university in engineering, a blue eyed blondie – a Vietnamese girl would have done it the year before, but she died of stomach cancer during her final year. Blondie’s still going strong. The intake at that university (Western Australia) is now 12% female; the intake at the Hong Kong universities that teach engineering is 50% female (no affirmative action for girls – in fact it was only after a public scandal/outcry/condemnation about 10 years ago that they stopped down-grading the results of female school-leavers on the grounds that ‘boys mature later’ so female school leavers have an ‘unfair’ advantage.) In that age group, Hong Kong has slightly more females than males, but the engineering working environment is still given as the deterrent for a small %.

    It’s easier now, but a first degree + minimum 5-6 years structured professional training is no longer enough.

  • http://blogs.discovermagazine.com/gnxp Razib Khan

    In your opinion, what would be the criteria for being noticeably smarter?

    well, they better seem smarter than me! my friend was definitely not smarter than me.

    I used to think it would be blindingly obvious when someone is brilliant (like 1 in 1000), but I am not sure anymore.

    i wouldn’t say 1 in 1000 is really brilliant. i mean, you can defend that term for them. but brilliant is as brilliant does…. and most people don’t do jack.

  • Sandgroper

    Highest income group in USA is 135-140, or around there?

    I’ve known one or two people who were up there and were big contributors; I’d categorise the late Peter Wroth as brilliant (and also a nice man) – engineering mathematician at Oxford. I’d guess he was around 150 or so, there was no subject he could not engage you on knowledgeably – if you wanted to talk about soccer, he would.

  • Sandgroper


    “Professors never die, they only lose their Faculties.” Sadly, he did.

  • Sandgroper

    Peter revolutionised modern soil mechanics when he wrote ‘Critical State Soil Mechanics’ with Andrew Schofield. It was a hard sell, because Karl Terzaghi was revered as the ‘father of soil mechanics’.

  • Violet

    #45 Fair enough. I guess it is easier with yourself as benchmark. Birds of same feather…. eh? :)

    #44 Sandgroper,
    I have heard that in olden days (in 50s or 60s) professors would deliberately fail about 50% of class so that the ones who get through are really all that. Now it is all grading on curve, so getting through doesn’t tell anything except for the basic capability (until the professional practice weeds out those who can’t take the heat).

    Terzaghi and Timoshenko were so highly revered that I inherited the first edition copies of their books on soil and structural mechanics intact. :)
    Emeritus Professor on my committee used to say that some topics need a co-evolution of other parts of theory/technology to be fully appreciated. His favorite example is how the pocket calculators revolutionized civil engineering practice and researchers were more “free” to develop equations that contained cube roots or such.

    Working with plasticity, nonlinearity on a daily basis needed personal computers I guess.

  • Sandgroper

    ‘olden days’ LOL :)

    Yes, you are exactly right, about all of that.

    Except that at my old university, in science, engineering and medicine, they are still using the old system. When my daughter went back to start her second year, more than 50% of the first year enrolment had disappeared. Failed. Gone. That was life science. By the time she started her third year, there were only two or three male students left – all of the rest had failed, including the ones who kept saying that girls can’t do science. She was very amused :)

  • http://neuroskeptic.blogspot.com Neuroskeptic

    Back to the original “Genius 4 year old” story, I think the reason these stories get headlines is that most people don’t know that IQ is age normalized.

    “4 Year Old With IQ 160” sounds much more exciting if you interpret it to mean “4 Year Old Could Outscore Adult With IQ 159 On Same Tests”.

    Also if you think about it, given that IQ scores are age normed, if anything the scores mean less, the younger you go.

    If you’re 4 years old and you have ‘the mental age of a 4 1/2 year old’ that would give you a very high IQ score because 6 months of development makes a lot of difference, at that age.

    But really it just means you’re a fast developer. It doesn’t necessarily mean you will end up that much smarter as an adult.

  • Sandgroper

    One of my classmates once asked one of our lecturers “What will be the pass % be for your exam?” and he answered “If you all fail, you all fail.”

    But it’s clear from my daughter’s experience that they are regrading, but still with a high fail rate.


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About Razib Khan

I have degrees in biology and biochemistry, a passion for genetics, history, and philosophy, and shrimp is my favorite food. In relation to nationality I'm a American Northwesterner, in politics I'm a reactionary, and as for religion I have none (I'm an atheist). If you want to know more, see the links at http://www.razib.com


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