Thursday, January 21, 2016

Estimating IQs Over the Official Ceiling

I just met a fellow who has taken over 100 IQ tests.  He claims IQ scores as high as 180 (D15). Of course, these tests are not properly normed, created by individuals, generally on very restricted developmental budgets.  This fellow, for example, admitted to scores between 135 and 180.  So, obviously, the reliability of these tests is highly suspect.

Tests such as the WAIS do render raw scores above the ceiling, which is 160.  However, they are over the ceiling for a reason.  After extensive analysis, they prove to be unreliable.  The independent tests often cannot undertake such analysis and have no reliable ceiling.

Still, what if you just must have some idea of by how much you exceed the ceiling.  I have developed two methods that may help you.

First, as you will see on my page H. macrocephalus, there seems to be a pretty good fit on cranial volume, for men at least.  We need to expand the study because there are few women at this IQ range and the few I found did not have huge noggins.

Anyway, you can estimate your cranial volume and then use the regression formula, IQ=20%V-181.  So, if you calculate a cranial volume of, say, 1,800 cc, you have a cranial IQ of 179.  That, however, is a ratio IQ, so your D15IQ is 158.  So, with this volume, you have no evidence that your IQ might exceed the ceiling of 160.

However, if your cranial volume is more than 1,850, then it will render a higher score.  Mine, adjusted for height is 1,993 which translates to 215 or a D15IQ of 177.  So, I have a data point suggesing that my IQ may be significantly over the ceiling.

Next, we know that the IQs of children are usually expected to regress to the mean by about 30% to 40% on the assumption that the heritability portion IQ subtracted from 1 equals the environmental portion that would be randomly distributed.  There are two things wrong with that.  First, very high IQs can be expected to be, at least in part, the result of rare recessives that will not perpetuate into the next generation.  In other words, we should expect some genetic regression.  Second, people tend to reproduce the environment in which they, themselves, were reared.  In other words, the assumption that, on average, two 140 IQ people will rear their children in a 50%'ile environment is flawed.  Empirical tests suggest that the regression to the mean is likely more like 25%.

Lastly, while it is controversial, women appear to have a standard deviation of 13.2 and men have 16.8.  Some researchers have found a different mean IQ, but that is still very controversial.  Because of this, for calculation purposes, calculations should be done on a standard deviation basis.  And, as we see in H. macrocephalus, it should all be calculated on a ratio scale.

My three children have a mean IQ of about 3.2 
σ and their mother about 1.8σ.  The implied mean of their mother and me is 3.2/.75=4.3σ.  From this, we can estimate my IQ at 4.3x2-1.8=6.8σ or a ratio IQ of 208.8 or a D15IQ of 170.
So, I could take the three values of 168, 170 and 177, average them and derive an IQ of 172.  It is interesting that when I read biographies, I feel the greatest kinship to Leibniz, who Cox, et alia estimated at 172 D15IQ.

However, when people ask me my IQ I tell them that I exceeded the ceiling on the IQ test that I took, so, over 160.  That leads to an interesting discussion about how come the Internet is so full of IQ scores higher than that.  That's a good discussion to have.

What I don't do is say 172 for the simple reason that I consider these calculations to be fun rather than reliable.  However since there is clearly a large population of high IQ people who want to know how much they exceed the ceiling, I will give you this.

I'm probably going to regret it.

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