Hacker News Reader

Comment by nradov | Hacker News Reader

Does intelligence follow the standard distribution?

> Does intelligence follow the standard distribution?

Intelligence may or may not. IQ, by definition, does.

IQ as an intelligence rank does indeed follow the standard distribution, but in practice IQ is estimated by tests. I believe the GP wanted to ask about a distribution of such "estimated" IQs.

Your score on an IQ test is reflective of your percentile amongst all IQ test takers. That is, if 50% of takers did better than you and 50% did worse than you, then you score a 100 (regardless of the actual number of questions you got right or wrong).

So, yes, IQ scores always necessarily follow a normal distribution - because that's how the scores are determined in the first place.

If that's true my IQ score is necessarily updated every time other takers take the test, because it necessarily depends on the current distribution right now. In reality such update happens very rarely and most IQ tests would give you a confidence interval instead, which is based on the distribution constructed via the past validations. There is no guarantee that those scores are indeed normal.

the parameters of the test scoring formulas are _by construction_ such that the IQ scores we find in the wild indeed follow the standard distribution. the scores. not the ticked boxes in the test sheets. but the "graded" evaluation.

If you actually look at common IQ tests like WAIS, you will find that's not true because they directly give the score (and confidence interval) and not the rank [1]. Their weights are indeed scaled in order to approximate the true distribution in advance, but individual tests may well have a different distribution.

[1] Compare with standardized tests with a similar principle, where your scaled scores are never available immediately. They are available only after collecting all raw scores to construct the reference distribution. No IQ tests I'm aware work like that.

I'm not sure what you mean to my understanding all tests are calibrated regularly every few years. and from that calibration they get the weights.

Are you saying you're sceptical about the calibration process?

Rather that it cannot be said simply "by construction" when the calibration only happens every few years. And I'm very sure that the calibration is done by sampling.

So IQ can be negative? (Normal distribution has non zero probability mass for all real numbers)

> IQ can be negative?

Theoretically, yes. We chose 100 as a midpoint for convenience. (Practically, there is a lower bound beyond which we cannot meaningfully interpret test results.)

Average intelligence does :)

I am pretty sure that the central limit theorem applies to a sample size as big as all living humans.

That isn't at all what the central limit theorem says. The whole point is it holds independent of the actual shape of distribution of the population. You could use the same argument to say social security numbers are normally distributed.

One way to explain things like height being normally distributed is that there are a bunch of independent factors which contribute, and the central limit theorem applied to those factors would then suggest the observed variable looking normal-ish.

IQ does, by definition.

Reply on news.ycombinator.com