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Comment by paulpauper | Hacker News Reader

This is why also claims of IQs above 180 or so are almost always BS, at least on normed tests. 6sd is about the maximum

It's also literally impossible for many modern tests. For example the WAIS-IV, a very popular measure, has a maximum possible FSIQ of 160. With a mean of 100 and an SD of 15, that's "only" 4 SDs from the mean (99.997 percentile).

And as you say, modern tests just aren't calibrated in that way. The WAIS-IV is calibrated for the 70-130 range [0]. It's used to provide broad ranges (e.g. 85-100 vs. 115-130), not to provide useful differentiations on the high end like 158 vs. 159.

In fact, the error increases with the score [1]. There is less certainty for a score of 145 than there is for 115. It's just not designed for separating geniuses from super geniuses or however you want to put it.

[0] https://www.quora.com/Whats-the-highest-IQ-score-you-can-get...

(Not a direct source I'm afraid, but the materials are proprietary.)

[1] https://en.wikipedia.org/wiki/IQ_classification#Giftedness

(There are several citations in this section, pertinent discussion below the table.)

Anything outside 70-130 is suspect in practice, as the tests aren't well calibrated beyond ±2σ.

I'm not sure what intellectual performance is even supposed to be implied by any given IQ score, given that the scores commonly used today are just a linear mapping from standard deviations above or below mean.

That said, on the low end at -3σ I would expect a serious deviation from a normal distribution just from the effect of dementia.

Sure, but the point is that 180 wouldn't make sense even if the test were perfect. There aren't enough humans on earth for that many standard deviations to exist in the first place. 180 IQ could as well be 2000 IQ, the sky is the limit when the scale makes no sense.

That's just wrong? 6 sigma would be IQ 100 + 6 * 15 = 190. 6 sigma is 1 in 506,797,346. So there should be 16 people with IQs that extreme if intelligence is normally distributed.

(There's a factor of two somewhere in here for the two tailed nature, but the point stands)

Either I'm misunderstanding the math, or you are. An IQ of 180 is 5 1/3 SD above mean, which is a bit more frequent than 1 in 26,330,254 (which would be 5.5 SD). Half that common because we're only talking about above, and 1 in 50m people on earth is still 160 people. That's not many, but I don't think it's negligible either.

https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rul...

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