I was unaware of the range restriction, which could well compress SD. That said, if you take the ‘9’ scorers as ‘9 or more’, then you get something like this (using 20-25)
Mean value is around 7 (6.8), 7% get 9 or more, suggesting 9 is at or around +1.5SD assuming normality, so when you get a sample size in the thousands, you should start seeing scores at 11 or so (+3SD) - I wouldn’t be startled to find Ben has this level of ability. But scores at (say) 15 or higher (+6SD) should only be seen with extraordinarily rarely.
If you use log-normal assumptions, you should expect something like if +1.5SD is 2, 3SD is around 6 (i.e. ~13), and 4.5SD would give scores at 21 or so.
An unfortunate challenge at picking at the tails here is one can train digit span—memory athletes drill this and I understand the record lies in the three figures.
Perhaps a natural test would be getting very smart but training naive people (IMOers?) to try this. If they’re consistently scoring 15+, this is hard to reconcile with normalish assumptions (digit span wouldn’t correlate perfectly with mathematical ability, so lots of 6 sigma+ results look weird), and vice versa.
I would be happy to take a bet that took a random sample of people that we knew (let’s say 10) and saw whether their responses fit more with a log-normal or a normal distribution, though I do guess this would be quite indiscriminate, since we are looking for divergence in the tails.
This random blogpost suggests that they stop at 9: https://pumpkinperson.com/2015/11/19/the-iq-of-daniel-seligman-part-5-digit-span-subtest/
I was unaware of the range restriction, which could well compress SD. That said, if you take the ‘9’ scorers as ‘9 or more’, then you get something like this (using 20-25)
Mean value is around 7 (6.8), 7% get 9 or more, suggesting 9 is at or around +1.5SD assuming normality, so when you get a sample size in the thousands, you should start seeing scores at 11 or so (+3SD) - I wouldn’t be startled to find Ben has this level of ability. But scores at (say) 15 or higher (+6SD) should only be seen with extraordinarily rarely.
If you use log-normal assumptions, you should expect something like if +1.5SD is 2, 3SD is around 6 (i.e. ~13), and 4.5SD would give scores at 21 or so.
An unfortunate challenge at picking at the tails here is one can train digit span—memory athletes drill this and I understand the record lies in the three figures.
Perhaps a natural test would be getting very smart but training naive people (IMOers?) to try this. If they’re consistently scoring 15+, this is hard to reconcile with normalish assumptions (digit span wouldn’t correlate perfectly with mathematical ability, so lots of 6 sigma+ results look weird), and vice versa.
Quick sanity check:
4.5SD = roughly 1 in 300,000 (according to wikipedia)
UK population = roughly 50 million
So there’d be 50 * 3 = 150 people in the UK who should be able to get scores at ~21 or more. Which seems quite plausible to me.
Also I know a few IMO people, I bet we could test this.
I would be happy to take a bet that took a random sample of people that we knew (let’s say 10) and saw whether their responses fit more with a log-normal or a normal distribution, though I do guess this would be quite indiscriminate, since we are looking for divergence in the tails.