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Modern IQ tests force test scores to fit a normal distribution, but I’ve long suspected the distribution of intelligence is anything but normal. After all, if you look at the distribution of wealth and income (a crude measure of intelligence), you find the richest people are worth millions of times more than the poorest. And that’s just because they’re not paying their fair share, as Elizabeth Warren would have us believe. We see the same skewed distribution in academic output, with the most productive scientists publishing orders of magnitude more than the least productive.

A member of Prometheus society once hypothesized that the human mind works in parallel, so that complex problem solving speed doubles every 10 IQ points (he later suggested 5)?

And yet at the same time, Arthur Jensen seemed to believe intelligence was normally distributed and in support of this cited cognitive measures that form a natural scale with equal intervals and a true zero point such as the total number of words a person knows or the number of digits they can repeat after one hearing, both of which were normally distributed. What was missing however from Jensen’s examples was complex on-the-spot problem solving.

Thanks to my research on how people today would score on the oldest Wechsler tests (the ancient WBI) I have some novel data on how long it takes people to solve visuo-spatial items. The WBI includes a subtest called Object Assembly where you have to fit a bunch of odd shaped cardboard cutouts together to make a familiar object, and over the past decade or so, this was administered to a relatively random sample of White young adults (n = 17). One seven piece item was easy enough that all 17 were able to complete it within the 3 minute time limit, yet hard enough that no one could solve it immediately.

Normally I wouldn’t show items from an actual IQ test, but the WBI is over 80 years old and Object Assembly is no longer part of current Wechsler subtests.

[update april 1, 2020, I decided to remove the photos to be safe, but it’s too bad because those were gorgeous photos I took]

When one test participant saw these cardboard cutouts being placed on the table, he apologized for being unable to contain his laughter. A painful reminder that my life’s work is considered a joke by much of the population. And yet for all their apparent absurdity, these silly little tests remain the crowning achievement of social science with one’s score being largely destiny .

Even on this one item, there seemed to be a correlation between IQ and occupation/education. The time taken to complete the puzzle ranged from 14 seconds (a professional with a Masters degree in Engineering from a top Canadian university) to a 137 seconds (a roofer with only a high school diploma). Below are the times of all 17 participants ranked from fastest to slowest.

14, 18, 21,30,31,33,34,35,48,58,60,65,68,69,82,89*,137

Mean = 52 seconds, Standard Deviation = 30 seconds

In a normal distribution, 68% fall within one standard deviation of the mean. In this distribution, 71% fell within one standard deviation of the mean (22 to 82 seconds) which is pretty damn close. Also in a normal distribution, 95% fall within two standard deviations (-8 to 112 seconds) and in my sample, 94% did (even closer!).

image found here

So simply by picking at least a moderately g loaded novel problem that is both easy enough that no one gives up, yet hard enough that everyone is forced to think, and measuring performance on a natural scale (time taken in seconds) a normal curve emerges, though a somewhat truncated one (the slowest time is much further from the mean than the fastest, perhaps because human hands can only assemble puzzles so fast, regardless of how quick the mind is).

To convert from time in seconds to IQ, all one needs to do is make the natural mean of 52 seconds equal to the IQ mean of 100, and make each natural standard deviation (30 seconds) faster or slower than 52 seconds, equal to 15 IQ points (the IQ standard deviation) above or below 100, respectively.

Thus the elite Masters degree in Engineering professional gets an IQ of 119 (14 seconds) and the high school only roofer gets an IQ of 58 (137 seconds). But note that even though IQ appears to be a true interval scale (meaning an X point gap between any two points on the IQ scale are equivalent), it is not a ratio scale, meaning IQs can not be meaningfully multiplied. So even though IQ 119 is about twice as high as IQ 58, the difference in actual problem solving speed is about an order of magnitude. This is because unlike height, weight and time in seconds to solve puzzles (which can be meaningfully multiplied) the IQ scale has no true zero point.

Of course the normal curve only applies to the biologically normal population, so it’s interesting to note that it’s now standard procedure to exclude pathological cases from IQ test norming samples. Indeed one man was excluded from my sample after he told me that years ago he had suffered a stroke (quite unusual for a man in his thirties). This man struggled greatly with the above puzzle, only joining 25% of the cuts within the 3 minute time limit. The only way to estimate what his time would have been had he not given up is divide 3 minutes by 25% which gives 12 minutes (720 seconds). This is more than 22 standard deviations slower than the mean of the normal sample, and equivalent to an IQ of -234! Such extreme deviations remind us how sensitive the normal curve is to the normality of the sample.

*one person solved the puzzle in 67 seconds, but the ear pieces were reversed, so only 75% of the cuts were correctly joined. I thus considered this equivalent to a perfect performance at 75% of the speed (67 seconds/0.75 = 89 seconds).