Commenter Philosopher wanted to know what I think Mug of Pee’s IQ is.

On college admission tests, Mug of Pee’s IQ equivalent is as high as 160, but on actual IQ tests like the Wechsler intelligence scale which he took at age nine, I crudely estimate Mug of Pee scored 127 (after adjusting for old norms).

Now, normally when someone has a huge achievement score > IQ score gap, they are described as overachievers, because they have learned far more than their IQ would predict.  Instead of humbly accepting this label, Mug of Pee has devoted his life to denying any distinction between IQ tests and achievement tests, irrationally claiming the SAT is the best IQ test and  pretentiously dismissing actual IQ tests as “soi-disant IQ tests”.

So what is his true IQ?

In order to answer this question, we must first note that IQ tests are largely considered valid to the extent that they measure g (general intelligence).  g is simply whatever causes all cognitive abilities to positively correlate.  The g loadings of the Wechsler and the SAT in the general U.S. population are not known, but by dividing their correlations with the Raven by the Raven’s g loading, it can be estimated that the Wechsler has a g loading of 0.94 and the SAT has a g loading of 0.68.  Further, based on the fact that Dartmouth students, largely selected based on SAT scores, regressed nearly half way to the U.S. mean on the WAIS, I estimate the WAIS and SAT correlate 0.52.

Armed with these three statistics, the following regression equation can be built (hat-tip to a member of Prometheus who suggested such equations to me many years ago):

Expected g Z score = 0.8(Wechsler Z score) + 0.26(college admission test Z score)

So, since I estimate Mug of Pee has a Z score of +1.8 on the Wechsler (IQ 127) and as high as +4 on college admission tests (IQ equivalent of 160), we’ll plug those values into the equation:

Expected g Z score = 0.8(1.8) + 0.26(4)

Expected g Z score = 1.44 + 1.04

Expected g Z score = 2.48

So on a hypothetically perfect measure of psychometric g, Mug of Pee would be expected to score 2.48 standard deviations above the U.S. mean (IQ 137).  We can say with 95% certainty that his true level of g is between 129 and 145.

 

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