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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 distri

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.

wavemode 2y ago
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.
- lifthrasiir 2y ago
  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.
froh 2y ago
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.
- lifthrasiir 2y ago
  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.
  - froh 2y ago
    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?
    - lifthrasiir 2y ago
      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.

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.

wavemode 2y ago

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.

lifthrasiir 2y ago
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.

froh 2y ago

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.

lifthrasiir 2y ago
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.
- froh 2y ago
  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?
  - lifthrasiir 2y ago
    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.