The boy who knew too much: a child prodigy

This is the true story of scientific child prodigy, and former baby genius, Ainan Celeste Cawley, written by his father. It is the true story, too, of his gifted brothers and of all the Cawley family. I write also of child prodigy and genius in general: what it is, and how it is so often neglected in the modern world. As a society, we so often fail those we should most hope to see succeed: our gifted children and the gifted adults they become. Site Copyright: Valentine Cawley, 2006 +

Sunday, March 11, 2007

The Great IQ Con

Perhaps you have taken an IQ test. Perhaps you scored well. Perhaps you think you know your IQ, then. It is probable that you don't, however.

You see IQ tests don't behave in the way that people expect. They don't actually measure the upper ranges of humanity very well, at all. In fact, they are a source of much mismeasure. The modern IQ test isn't equipped to ascertain the most gifted among us at all - in fact, it is almost as if they are designed to hide them. Perhaps that is exactly what is happening.

I should explain. Everyone has heard the phrase "ceiling effects" - but there is much more to it than this. Firstly, when do ceiling effects invalidate the test result? One researcher put it that if you have answered 90% of the test items then that test cannot measure your IQ. The result is invalid. Indeed, an IQ test can only give an accurate result if you are able only to answer HALF the questions. The higher your point of failure to answer is above that, the less accurate the result will be.

When else might we see ceiling effects? If you scored in the 99th percentile on ANY subtest, then that test is, more than likely, underestimating your score. It cannot determine how much beyond that score you would have scored in a test with a higher ceiling. This is important to note. Just because this has happened, does not mean your score - or your child's score would have been astronomically beyond the ceiling - it might be in the right place after all - but it is more than likely that it is an underestimate - and it could be a very great discrepancy indeed. There is no way of knowing.

That seems bad enough. But wait until you hear about what they do to the "norming". Did you know that the number of extremely gifted individuals is higher than expected for a normal distribution of intelligence? Did you also know that the number of extremely intellectually impaired individuals is much higher than expected too? In a rational profession, given to promoting truth, above convenience or dogma, you would have thought that psychologists would acknowledge this...but no. What do IQ tests do? They eliminate the phenomenon by cheating the test.

What I mean by this is that the norms of the test impose an artificial correction of the results to eliminate the unexpectedly high number of extremely gifted scorers. They "compress" the upper scoring range to fit a normal curve, artificially "re-norming" or depressing high scores. Basically, modern psychometric tests steal IQ points from you, by pretending those points don't exist: they are simply squashed out of existence.

How many points are lost in this fashion? I have seen one estimate, by a psychologist not happy about the situation, placing the discrepancy at 25 points, for high scorers. This means someone who would have scored 180 - and been labelled "profoundly gifted" - may be renormed to score 155 - a much more common seeming score.

In practice, how much discrepancy do all these effects add up to? Prepare to be shocked - but first place an estimate on it yourself and see just how honest and fair to the gifted population modern psychometric testing is.

Got a number?

Well, the measured difference on real life test cases between some extremely gifted children measured on old style tests, with higher ceilings - and modern tests with much lower ceilings is - an unbelievable 85 to 107 IQ points.

That means something very clear. The most gifted segment of the population will not now be identifiable - but will score similarly to those who are moderately or slightly more gifted.

One real life example scored 120 points on a WISC test. The same person scored 220 on an old Stanford Binet LM. Now, that is disturbing. For the child would not have been admitted to a gifted program on the basis of the first score - yet was clearly very profoundly gifted when measured on a test with a higher ceiling.

Remember this: you DON'T have to score at the top of a test, to be affected by the ceiling. Ceiling effects get stronger the closer you get to the end of the test - but make the test totally invalid by the time 90 per cent of the test items are answered. Yet, long before that point, they could be making a significant difference to the results.

IQ is not what it was - and it never was what we thought it was, anyway. What a con.

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posted by Valentine Cawley @ 5:04 PM 


Anonymous Anonymous said...

Hi Valentine:
I have been hoovering around for a while. Really enjoy your writing.
I have a very gifted mathematician in my household. Never tested his IQ (don't they say that the most accurate IQ test is the one administered before the formal schooling starts ?), but on subject test he always scores 99%. So he participated in talent searches (USA), that give above level tests and compare the results with high school students. This gave me an idea about where he actually places with his ability.


P.S. I so agree with your reference to "teaching to the left" in US schools. I was "schooled" in Europe and think that they do the opposite there

3:40 AM  
Blogger Valentine Cawley said...

Yes. Later tests have more of a ceiling effect for many gifted kids.

I would think that the most relevant information for your son is how he does in maths...since he is a mathematician. I wouldn't bother too much about IQ tests given their huge range of problems and limitations.

Thanks for your kind remark re. my writing.

Yes, Europe is more challenging in its education. Perhaps I should write more on that.

Best wishes

7:15 AM  
Blogger EbTech said...

My parents had me take a professional IQ test when I was very young. I maxed out the test, so my real IQ remains a mystery...

The ceiling effect is also a problem in schools with grade inflation. It's not so bad in the UK; but in North America, top universities are forced to choose which applicants to accept among averages of 99% or higher. One of the dangers here is that a single failure may irreparably damage a student's grade point average.

In response to your concerns about norming, it's not maliciousness on the part of IQ testers; it's simply the way IQ is defined, and probably makes more sense than the older ratio tests. It's not easy to describe intelligence with a number. Does an IQ of 200 signify twice the intelligence of someone who scores an average 100? Do IQs of 170 and 180 signify the same relative difference as IQs of 70 and 80?

If there are so many people at the extreme ends of the curve, then perhaps a logistic distribution model would be more fitting than a normal distribution. If anyone is curious as to what their IQ would be according to this distribution, it's possible to derive a conversion formula. Perhaps I will try it when I have time...

2:12 AM  
Blogger EbTech said...

If my algebra is correct, the normal-to-logistic conversion formula (with mean = 100, standard deviation = 15) is:

Y = 100 + 15*sqrt(3)/pi*ln(2/(1 - erf( (X - 100)/(15*sqrt(2)) ) - 1)

where X is the normal-curved IQ, Y is the equivalent logistic IQ, and erf() is the error function. Here are a few sample conversions:

X = 40, Y = 14
X = 60, Y = 54
X = 80, Y = 81
X = 100, Y = 100
X = 120, Y = 119
X = 140, Y = 146
X = 160, Y = 186
X = 180, Y = 239
X = 200, Y = 307

You were right: there is a huge disparity at the upper and lower ranges. While the normal model predicts the world's smartest person to have an IQ of about 200, the logistic model predicts a maximum IQ of about 300. You might be interested to know that many tournaments use the logistic model to rate players, so perhaps it is the more accurate choice after all.

The nice thing about this formula is that it effectively undoes the norming which you were unhappy about. Of course, it does nothing to remedy the ceiling effect. The only way to fix that is by taking a more difficult test.

9:20 AM  
Blogger Valentine Cawley said...

Thanks for the maths.

Your thought agrees with my own observations: I think that human variation is greater than a ceiling of IQ 200 would indicate...even history has suspicious examples of people who might be beyond it (Try Sidis, Da Vinci...)

I have the feeling that there is, for practical reasons, no real limit in that the right combination of factors could even push the result out further (though of course there will be real limit the max computational power of a human brain design etc...but I think it is greater than one might suppose.)

Thanks for your learned comment.

10:25 AM  

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