[This article was updated on Januaaryn 18, 2021 to include additional data I learned of in the comment section]

Commenter “Carlos” left a number of comments on this blog about his brilliant cousin. These comments are posted below in red.

On September 10, 2020, commenter “Carlos” wrote:

Hi Pumpkin Person! I’ve been reading you since too long and now i have an intersting case for you
My cousin is pretty brilliant and I’ve been observing him for quite a long time. I would like your estimate on his IQ. Here it goes his history: at 5 years old he memorized around 200 country flags in a book,and was able to draw any flag at any time. At 16 years old he memorized 200 pi numbers in a couple of hours. In high school he was the best math student despite lack of effort (in fact he doesnt like studying).He started musi. College at 18 and now at 20 is able to play around 30 instruments with greatness. He does extremely fast mental calculus. Since I’m really intersted in IQ testing, I tried something with him. At 16 years old I sat him the Raven standard progressive matrices, which he achieved 60/60. Later, at 18, he passed mensa test,but I dont know what test was used neither the score, and later marked 36/36 on Raven advanced matrices. He even said it was too easy. Last week I showed him your PATMA test, and in less than 5 minutes he got 10/10. I tried the digit span with him and he was capable of doing 9 forward and 8 backwards, but had one fail: when he had to repeat 8 digits backwards, he got one right and one wrong, saying he could not hear properly the one he got wrong (I didnt try any more than this).ohh I also tried with him the arithmetic part of WAIS IV, in which he was able to get everything right, answering every question in under than 10 seconds)…. The only other information I have is about a high range IQ test called Sigma Test. He did from the 1 to 20 easily, with no difficulty, but was quite lazy to do anything more.

I’d really enjoy your study in this case.

Greeting from London!

My first question is how did Carlos sit his cousin for the Raven Standard Progressive Matrices & the WAIS-IV arithmetic test? Does he have access to these tests?

On Sept 11, 2020, he wrote:

Yeah, I’m not making up. He’s really my cousin! I have always been curious about him and his real IQ. His father is also gifted, but waaaay less than him. Another thing I remembered is that he is able to speak any words backwards very fast. People are always asking him to do it, because it’s really fun to see. He was born here in London but lived some time in Paris, as his father is an engineer and was moved

On Jan 4, 2021, Carlos wrote:

Some time ago I posted a comment talking about my cousin Brian, who has exceptional intelligence. Yesterday I found out he was evaluated with WAIS IV this year, january, at 20 years old. The raw scores:

Vocabulary: 45/57
Similarities: 34/36
Information: 23/26
Matrices: 26/26
Visual Puzzles: 23/26 (Carlos later said he made an error & actual score was 25/26)
Block Design: 66/66
Digit Span: 45/48
Arithmetic: 22/22
Coding: 98/135
Symbol Search: 49/60

He is a musician and is studying to become an orchestra conductor. He plays very well around 25 musical instruments and has great memory skills.

As you can see he excelled Arithmetic (all the questions answered in less than 10 seconds, according to his psychologist), matrices subtests and Block Design, so I’m going to give you some other informations so you can try a better estimate.

Her psychologist administered some WISC V subtests, as they are pretty hard (even more than the WAIS IV) he excelled the Matrix Reasoning part and had a 51 on Digit Span. Also had a 33/34 on arithmetic. Arithmetic on WISC V is way harder than arithmetic on WAIS IV, but the norms are a bit awkward. Maybe you can try to extrapolate. There is a extended WISC V norms on internet, just search for it and its easy to find.

Some months ago I showed him your PATMA. He had 10/10 with no efforts. He took the Raven Advanced matrices with 18 years old and scored 36/36 on the 40 minutes version.
Also he took the Cattell Culture Fair Form B with 18 years old and scored a very high 42 out of 50 questions (her mother couldn’t recall exactly). Also scored 43/44 on D70 and 44/44 on D48 tests.

I think it would be great if you show us your estimative about him, as he had some ceiling problems with WAIS IV.

Carlos’s cousin sounds ridiculously intelligent and the fact that he’s an aspiring conductor reminds me that Arthur Jensen viewed conductors as men of high intelligence. “The musicians in the symphony orchestras are kind of average” he told Forbes magazine’s Daniel Seligman. “They’re at about the level of an average BA graduate. But the conductors–now they’re something else again.”

But I’m surprised he took the WAIS-IV in January 2021. Aren’t we in a pandemic? Did he and the psychologist wear a mask or was the test administered by zoom? The latter seems unlikely since Block Design was administered.

Nonetheless, using the raw scores Carlos provided, I converted his cousin’s WAIS-IV scores to scaled score & IQ equivalents (isn’t this the job of the psychologist who tested him?). I’m assuming he took the American version. Note that the subtests are expressed as scaled scores where the U.S. mean and standard deviation at all age groups are set at 10 and 3 respectively. By contrast, the index scores and full-scale IQ use a scale where the U.S. mean and SD are set at 100 and 15 respectively.

	scores before Flynn effect adjustments	adjusted for the Flynn effect
Vocabulary (word knowledge)	14	12.73
Similarities (verbal abstraction & thought organization)	17	16.11
Information (long-term memory & environmental awareness)	17	16.36
Matrices (visual pattern recognition)	18 (24 using WISC-V scores)	17.24 (23.84 using WISC-V scores)
Visual Puzzles (spatial reasoning)	17	16.62
Block Design (visual organization & spatial analysis)	19	18.62
Digit Span (rote memory & attention)	19 (22 using WISC-V scores)	18.62 (21.9 using WISC-V scores)
Arithmetic (mental math)	19 (17 using WISC-V scores)	19 (17 using WISC-V scores)
Coding (rapid eye-hand coordination)	15	14.75
Symbol Search (visual scanning)	16	15.75
Verbal comprehension index	136	130
Perceptual Reasoning index	146 (150+ if we substitute WISC-V scores for Matrices)	142 (150+ if we substitute WISC-V scores for Matrices)
Working Memory index	150+ (150+ if we substitute WISC-V scores for Digit Span & Arithmetic)	150+ (150+ if we substitute WISC-V scores for Digit Span & Arithmetic)
Processing speed index	129	129
Full-scale IQ	151 (157 if we substitute WISC-V scores for Matrices, Digit Span & Arithmetic)	148 (154 if we substitute WISC-V scores for Digit Span & Arithmetic)

As the above data shows, Carlo’s cousin has an overall WAIS-IV IQ of roughly 150 (before and after corrections for the Flynn effect). This puts him at the extremely brilliant range and sounds consistent with his spectacular intellectual achievements.

Although he hit the WAIS-IV raw score ceiling on three subtests (Arithmetic, Matrices & Block Design) and the WAIS-IV scaled score ceiling (19) on three subtests ( Arithmetic, Block Design & Digit Span) it was not immediately obvious that his WAIS-IV full-scale IQ was supressed by ceiling bumping. My general rule for ceiling bumping is when at least half the subtests hit the scaled score ceiling or there’s a non-trivial median scaled score > mean scaled score gap. Carlos’s cousin meets neither of these criteria for full-scale IQ but he does meet the first one for Working Memory index.

Thus it’s interesting that the psychologist administered the Matrices, Digit Span and Arithmetic subtests of the children’s scale (WISC-V) because these now have super high ceiling norms (above scaled score 19) for identifying profoundly gifted kids. Unfortunately at age 20, Carlos’s cousin is too old for these norms but if we use the norms for U.S. 16.95-year-olds, his WISC-V Digit Span gets a scaled score of 23 (roughly one in 136,000 level)! However given that he was presumably 20-years-old, I would reduce this to 22 (roughly one in 31,000 level). Given that these extended norms were published in 2019 (and likely gathered circa 2017?) one might reduce this further to 21.9 for the Digit Span Flynn effect.

Meanwhile on the WISC-IV Matrices subtest, he obtained a scaled scored of 24 (about one in 652,000 level!) and because performance on this task (at least at the high end) does not increase from age 16.95 to age 20, there was no need to adjust for age, though after Flynn effect correction it became 23.84.

After acing the WAIS-IV Arithmetic subtest and the PATMA, Carlos’s cousin regressed to the mean on the WISC-V Arithmetic subtest. The extended norms don’t show equivalents below a scaled score of 18 but if they did, Carlos’s cousin would have likely scored 17 for 16.95-year-olds (one in 100 level) and this should be reduced to 16 assuming he was 20-years-old. Arithmetic shows no Flynn effect so no need to adjust for slightly old norms.

Too bad the psychologists apparently did not give the WISC-V Block Design to see if he could have exceeded a subscale score of 19 on that subtest too, although given the high practice effect of this subtest, it would have been unwise to administer it so soon after the WAIS-IV version.

Although Carlos’s cousin was above average on all subtests, he scored relatively low on Vocabulary. Given that Carlos appears to be Hispanic, I wonder if his cousin is bilingual and if that may have supressed his English vocabulary.