[WorkLifeBalance]

The difference between 99th and 99.99th percentile is 1.4 standard deviations, a common IQ test ought to be able to be accurate to that. Otherwise it couldn't measure the difference between 100 and 120 IQ (0 to 1.4z) which it clearly can.

[gjm11]

I don't think your reasoning is valid. A test might be unable to discriminate accurately at the extremes not because it's uniformly too inaccurate but because it doesn't have enough range.

Toy model: the test consists of one question that everyone in the top 1% can do and no one in the bottom 99% can do; one question that everyone in the top 2% can do and no one in the bottom 98% can do; ... one question that everyone in the top 99% can do and no one in the bottom 1% can do. This test discriminates very nicely and accurately throughout its range of applicability, but it will do no good at all from distinguishing a top-0.01% person from a merely top-1% person.

(Just as a tape measure 2m long will let you compare people very accurately by height provided they're no taller than 2m, but will be much less useful for people taller than that.)

[WorkLifeBalance]

Modern tests are delivered by computer and typically are adaptive. This means that as you answer questions correctly you get asked increasingly difficult questions until you get some wrong.

This means that you aren't limited to asking the same questions to everyone so you can have appropriate discrimination through the range.

[diminoten]

> a common IQ test ought to be able to be accurate to that

Accurate to what, even? The very notion of IQ is fuzzy, so naturally any test trying to measure the value would inherit that fuzziness.

The difference between 100 and 120 may be statistically identical to 99 and 99.99, but the practical difference is vastly different. At a certain point, the IQ test is "defeated", and any value above a certain threshold is nose.

[SiempreViernes]

Sorry, I don't understand: how do you know the percentile difference in terms of standard deviations but not know if a test is accurate enough?

[LukeShu]

By assuming that it's a normal distribution.

[npunt]

An answer, by analogy-

If you yell into a microphone, the recording will come out distorted and inaccurate. Yet if you speak normally into one, the recording will sound rather true to life. This is because the microphone has been tuned to a certain level of sensitivity, and when that threshold is exceeded, what it records is clipped.

A similar principle holds for many types of human tests in education, psych, etc.