Not exactly Gaussian—that’s even theoretically impossible because a Gaussian has infinitely long tails—but approximately Gaussian. Bell-shaped, in other words.
An IQ test in which the scores are only normalized linearly is a worse approximation to a Gaussian distribution than one which is intentionally designed to give Gaussianly distributed scores.
It assumes that all the variables you’re summing are independent.
Weaker forms of CLT hold up even if you relax the independence assumption. See Wikipedia for details.
As a practical matter, in IQ testing even with only linear normalization of raw scores you will get something approximately Gaussian.
I wouldn’t count on that more than about one standard deviation away from the mean.
Not exactly Gaussian—that’s even theoretically impossible because a Gaussian has infinitely long tails—but approximately Gaussian. Bell-shaped, in other words.
Fallacy of grey. Certain approximations are worse than others.
So in this particular example, which approximation is worse than which other approximation and by which metric?
An IQ test in which the scores are only normalized linearly is a worse approximation to a Gaussian distribution than one which is intentionally designed to give Gaussianly distributed scores.
Well, duh, but I don’t see the point.