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by hackandthink·3y ago·view on hn ↗
Did not know:

"correlation is 80% between test and retest, meaning you being you explains less than 64% of your test results"

"IQ decorrelates as it goes higher"

"So “very low IQ” may provide information, while “very high IQ” may convey nothing better than random"

1 comments
Did not read the article but to react to this point:

> "IQ decorrelates as it goes higher"

That is to be expected.

Let's say as an example we model performance as the equal sum of two gaussian distributed variables - inborn, static ability that changes between people, and how well someone is feeling on the day of the test. This is similar to how ELO scoring works in chess and video games.

In this case let's say a person scores 3 standard deviations above the average - this could either mean that person has 3 StdDev ability and an average day (a probablity of about 0.1%) OR he has 2 StdDev ability (2%) with an 1 StDev 'lucky' day (16%) for a probability of 0.3%.

This means, the further off center we go in the distribution the larger the proportion of the 'lucky' people will be, compared to innate high scorers.

Gaussian distributions are symmetrical, which means every argument about what happens at the high end equally applies to the low end. That's not what the article says: it says the low end (far below the mean) is highly correlated with performance, but the high end is not. By your argument, someone with an IQ of 70 should be more likely to be simply having a bad day than to have a natural "intelligence" (whatever TF that means) truly at that level.

Edit: On second thought, the argument works a little better if you assume that the variance of the "daily fluctuation" distribution is proportional to the magnitude of the "innate" one, so someone with an "innate" 70 varies +/- 7 per day, but someone with an "innate" 150 varies +/- 15.

> Gaussian distributions are symmetrical, which means every argument about what happens at the high end equally applies to the low end.

That's only relevant for the shape of the distribution. Any usage of the distribution will certainly include a comparison operation which is not symmetric across IQ 100.

Interesting point. It seems to be related with regression toward the mean.