Earlier I blogged about the freakishly high scores commenter “Jesse Watters” claims to have obtained on the WAIS-IV IQ test.

As I explained in that post, the WAIS-IV is an IQ test that actually consists of 15 mini IQ tests (subtests), however to differentiate the subtest scores from overall IQ scores, the subtest scores are expressed as scaled scores.  Unlike the overall IQ scores, which have a mean of 100 and a standard deviation of 15 in the U.S. population, the scaled scores have a mean of 10 and an SD of 3, and as commenter Animekitty noted, can be converted to IQ equivalents by multiplying by 5 and then adding 50.

So for example, a scaled score of 16 is equal to an IQ of 130 (top 2%).  Many people think that if your average scaled score on WAIS-IV subtests is 16, that your full-scale IQ is 130, but in fact your full-scale IQ would be 143 (the top 0.2%).  That’s because  far fewer than 2% of the U.S. population can perform in the top 2% in at least half of all brain functions measured by the WAIS-IV, which is typically required to average in the top 2%.

Roughly speaking, full-scale IQ = 6.97057(average scaled score) + 31.533486.

Typically only 10 core subtests are used to calculate the full-scale IQ but there are 5 supplementary subtests that are more or less interchangeable with the core subtests, and in Jesse’s case, it is useful to look at them all..

Now because Jesse claims to have obtained scaled scores of 19 on most of the WAIS-IV subtests, his average scaled score (18.73) is misleading because the maximum scaled score the WAIS-IV provides is 19, thus spuriously imposing a ceiling on his average scaled score.

However Jesse also provided raw scores on each subtest, so I looked at these to find evidence that he could have scored beyond 19 on some subtests if the WAIS-IV had allowed it.  I found evidence that if the WAIS-IV allowed it, he could have obtained a scaled score of at least 20 on the subtests known as Similarities, Information, Comprehension, Symbol Search,  Cancelation, Digit Span, Letter-Number Sequencing, and perhaps several more subtests had they included harder items.

Especially impressive was the 30/30 raw score he claims to have obtained on Letter-Number Sequencing, because only 27/30 is required to get a scaled score of 19 in Jesse’s age group (18-19).  Now without revealing too much about this subtest, it’s one of those uncommon psychometric tasks that increases in difficulty in a very quantifiable objective linear way, at least once you get past the easier items , and as a result, there was a very steep but linear increase in scaled scores as a function of raw scores, once you make it to the hardest third of the test.

From this linear relationship, I calculate that had the WAIS-IV allowed for scaled scores beyond 19, Jesse’s raw score of 30/30 would have equated to a scaled score of 23.5!  And even that might be an underestimate because he correctly answered every single item, allegedly.

Now Jesse claims that his lowest WAIS-IV scaled score (Vocabulary) was 17.  If we conservatively assume that if the WAIS-IV had unlimited ceiling, his highest scaled score would be 23.5 (Letter-Number Sequencing), then we might very crudely guess that on a ceiling-free WAIS-IV, his average score would be half-way between both extremes: 20.25

Invoking the formula above:

Full-scale IQ = 6.97057(average scaled score) + 31.533486.

Full-scale IQ = 6.97057(20.25) + 31.533486.

Full-scale IQ = 173

This is somewhat higher than the full-scale IQ of 168 I had estimated for Jesse in my earlier post, assuming his claims are true, but that was before he claimed a perfect raw performance on Letter-Number Sequencing.  If these claims are true, then 173 (U.S. norms) is a better estimate, and a conservative estimate, though James Flynn would probably argue it should be reduced to 170 because if I’m not mistaken, WAIS-IV norms are nearly a decade old.

There are only about 519 Americans with IQs of 170+ but because a lot of them are children or older adults, and because IQ is normed for age, they wouldn’t need to perform as well as Jesse allegedly did to obtain their 170+ IQs.  The fact that Jesse allegedly obtained this IQ while being in the peak age group for raw brain power, suggests that in an absolute sense, he might be one of the 100 smartest people in America!

If he’s telling the truth 🙂