[FabHK]

hmm, interesting.

Case 1: IQ tests are of the form:

    100 + 20 x F_N^-1( F_R(R) )

where R is a raw score, that score is then translated into a percentile (by the cumulative distribution function F_R), and that is then translated into a gaussian ~N(100, 20^2) (by the inverse pdf F_N and constants 100, 20).

Case 2: IQ tests are of the form

    c1 + c2 x R

where R is a raw score and c1, c2 are chosen such that E[R] = 100, Var[R] = 20^2.

If what is actually done is case 1, then what you say is correct, and saying "IQ is normally distributed" has no empirical content.

If what is actually done is case 2, then saying "IQ is normally distributed" translates to "R is normally distributed" and has some empirical content. In particular, R (thus IQ) might not be normally distributed.

(The article seems to argue, but doesn't make the case that case 1 is the case.)

EDIT to add: dunno what the Variance is actually, might be 15^2 rather than 20^2.