I finally took a look at the statistics of the readers who took the PAIS Information subtest; in particular, the subset of 18 who also reported Wechsler IQ scores (r = 0.43).

PAIS Information	Wechsler IQ equivalent (equipercentile equating)
12	103
17	111
19	131
21	140
22	141
23	144
25	149
26	150

The PAIS Information was originally normed on 16 native born English speaking Canadians at a local pool hall and these had a mean of 12 (SD 3.4). However because Canadians are a bit smarter and less variable than Americans, this was adjusted to 11.3 (SD 3.5) to be comparable with the U.S. norms of the Wechsler. These norms may underestimate the IQs of my readers because the readers took the test on computers and thus had to spell the answers, while the pool hall sample just had to say them. While I tried to allow for common spelling mistakes, I could not anticipate all the misspellings that would occur.

On the other hand, the norms my overestimate the IQ of my readers because from reading my blog or sharing my interests, my blog readers know a lot of the stuff that I know which gave them a bit of an advantage over the pool hall sample. These two biases largely cancel each other out.

If we equate 11.3 with IQ 100 and 3.5 with 15 IQ points, then the 18 blog readers have a mean of 137 (SD 14.6), only 6 points higher than their self-reported Wechsler scores. However the real difference between the two norming methods becomes much greater at the extremes.

Using the pool hall derived data, the 18 readers have an IQ range of 103 to 163 but using the range of their Wechsler scores, they have a range of 103 to 150.

It seems the two methods give similar results close to IQ 100 but become increasingly divergent at the extremes. What explains this? Although both methods define IQ as Z(15) + 100, Wechsler IQs are largely derived from normalized Zs, that is Z scores that are FORCED to fit the bell curve. while the other method calculated Z scores normally. It seems that when you force IQ (and many other trait for that matter) to fit a bell curve, you limit variation at the extremes. For example, before the Wechsler scales started forcing scores to fit the normal curve, he noted they showed a Pearson IV distribution, though this had little effect on the vast majority of IQs..

Childhood age ratio IQs where IQ is just your mental age calculated as a percentage of your chronological age yield IQs as high as the 220s! Jensen argued that IQ is normally distributed from 50 to 150 but beyond these extremes, there’s are more people than the normal curve predicts. John Scoville hypothesized that childhood ratio IQs might follow a log-normal distribution causing the distribution to appear normal at the middle of the curve, but deviate as one moves to the extremes.

My own intuition tells me that non-normal distributions might be an artifact of using culturally loaded/crystallized tests. There might be something about biologically extreme minds ending up in culturally extreme environments that causes the surplus at the tails of the curve.