The normal distribution is just a model. You have to be very careful about expectations that happen at 6 sigma. Nothing guarantees your gaussian works well that far from the mean.
Yes, but leplen’s point is that the construction doesn’t map directly to reality. An ‘IQ score’ is not calculated by lining everyone up by raw score and determining where they fall; we create a mapping from raw scores to IQ from a reference distribution, and then compare people’s scores to the distribution.
As you might expect, the IQ tests start to lose statistical validity as you go further and further into the extremes. How well can we differentiate a person of 175 IQ and 190 IQ with our current tests? Not nearly as well as we can differentiate a person of 95 IQ and 110 IQ.
And the biological model of what makes people score particular ways on IQ tests looks normally distributed from afar, but is that true everywhere? Obviously not in certain cases (think of stuff like Down’s), and so possibly not so in the upper extreme, as well.
The normal distribution is just a model. You have to be very careful about expectations that happen at 6 sigma. Nothing guarantees your gaussian works well that far from the mean.
Isn’t IQ normally distributed by construction?
Yes, but leplen’s point is that the construction doesn’t map directly to reality. An ‘IQ score’ is not calculated by lining everyone up by raw score and determining where they fall; we create a mapping from raw scores to IQ from a reference distribution, and then compare people’s scores to the distribution.
As you might expect, the IQ tests start to lose statistical validity as you go further and further into the extremes. How well can we differentiate a person of 175 IQ and 190 IQ with our current tests? Not nearly as well as we can differentiate a person of 95 IQ and 110 IQ.
And the biological model of what makes people score particular ways on IQ tests looks normally distributed from afar, but is that true everywhere? Obviously not in certain cases (think of stuff like Down’s), and so possibly not so in the upper extreme, as well.