[froh]

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]

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]

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]

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.