There’s been a lot of talk in my Twitter timeline about Boris Johnson and IQ lately. Apparently the Mayor of London thinks that some people really are more worthy than others. This controversy spilled over into the comments of a Language Log post, and commenter Ran Ari-Gur said the following (which I can’t verify):

So it’s not that IQ is an expression of some normally-distributed variable, with just the mean and standard deviation being arbitrarily assigned certain values (100 and 15); rather, it’s that IQ is an expression of some variable of unknown distribution, with all percentiles being arbitrarily assigned values according to what they would be if the variable were normally distributed with μ = 100 and σ = 15.

Think about that for the moment. Lots of people (including, most notably, Herrnstein and Murray in the title of their book) either claim or implicitly assume that not only is Spearman’s g something that is actually real (Gould’s “fallacy of reification”), but that it’s actually a normally distributed random variable. Is it? What evidence do we have for that? Evidence that’s actually independent of these IQ tests that are normally distributed by construction? I haven’t studied the literature, so I honestly don’t know the answer to this.