Commenter Billy was kind enough to share with us the raw scores he obtained on the WAIS-IV and I have converted these into scaled scores and composite scores. I apologize to the other people who have also asked me to do this for them, but Billy just happened to ask when I had more free time and his demographics make him a unique case study.

Billy is a young American black man born to an upper-class immigrant family. Despite spending his early childhood in sub-Saharan Africa and not learning English until coming to the U.S. at around age eight, Billy obtained one of his highest scores on the culturally loaded Vocabulary subtest.

Below are Billy’s scores. Note that the subtests are scored on a scale from 1 to 19, where 10 is the U.S. mean for one’s age and 3 is the standard deviation. This is comparable to the distribution of male U.S. height, where in the peak age group, the mean is about 10 inches (above five feet) and the standard deviation is about 3 inches.

Presumably Billy took the WAIS-IV circa 2020 (14 years after it was normed). Because older tests tend to give inflated results, in the far right column I have adjusted all of the scores for the Flynn effect. The unadjusted scores are probably too high but the adjusted scores are probably too low because the Flynn effect might not be as large as folks think and may have plateaued or even reversed since 2006 (we’ll know better when the WAIS-V comes out).

scores before Flynn effect adjustmentsadjusted for the Flynn effect
Vocabulary (word knowledge)1917.73
Similarities (verbal abstraction & thought organization)19+18.11+
Comprehension (socio-understanding & common sense)1716.49
Matrices (visual pattern recognition)1817.24
Visual Puzzles (spatial reasoning)1413.62
Figure Weights (quantitative comparison)1716.24
Digit Span (rote memory & attention)1716.62
Arithmetic (mental math)1212
Coding (rapid eye-hand coordination)98.75
Symbol Search (visual scanning)1514.75
Verbal comprehension index150+145+
Perceptual Reasoning index136133
Working Memory index125125
Processing speed index111111
Full-scale IQ141+138+
Adjustments for Flynn effect were made using page 240 of Are We Getting SMARTER? by James Flynn. I assumed that the rate of change that occurred between the norming of the WAIS-III (1995) and the WAIS-IV (2006) has continued to 2020. Flynn had no data for Visual Puzzles, Figure Weights or Symbol Search so rates for Block Design, Matrix Reasoning & Coding were assumed for each of those subtests respectively.

Normally the WAIS-IV includes the subtests Information (general knowledge) and Block Design (spatial analysis) but for whatever reason, Billy’s examiner decided to use optional subtests (Comprehension and Figure Weights) respectively. Such substitutions are allowed as long as the examiner makes them a priori, and not to help or hurt a particular subject’s scores.

Billy wrote the following in the comment section:

Like I said, it’s unofficial, so I was tested out of convenience; not from a professional. Though my personal reason outside of knowing my IQ is knowing where I’m deficient – or my cognitive profile. Based on my Mensa scores, a wonderlic at 75th percentile while a passing RAIT score just doesn’t hint at a stable profile for me. I seem to have a hard time concentrating on tasks, so I figured it’s probably a working memory and or processing speed issue. I’ve never been tested for a mental illness.

Billy’s profile shows Verbal Comprehension > Perceptual Reasoning > Working Memory > Processing Speed.

Unfortunately the WAIS-IV lumps Visual Abstraction (Matrix Reasoning and Figure Weights) into the same category as Spatial Reasoning (Visual Puzzles) creating a meaningless hybrid known as “Perceptual Reasoning index”. However if we untangle these two abilities, we see that Billy’s Visual Abstraction is almost as high as his Verbal Comprehension (both domains are highly g loaded) and that his Spatial Reasoning is somewhat lower than his Working Memory.

He’s comfortably above average in all domains, but his weak point is Processing Speed, probably because this is the least g loaded domain. It might also imply a weakness in Executive Function, but we’d need neurological testing to infer that. His very superior score in Comprehension implies high social intelligence; on the other hand Comprehension was lower than his other Verbal Comprehension scores. Had the WAIS-IV not foolishly removed the Picture Arrangement subtest, we’d have a fuller look at his social cognition.

Billy’s relatively low scores on Processing Speed and Arithmetic probably explain why he underperformed on the Wonderlic, a speed based test with a lot of number crunching.

Overall Billy is a man of incredibly high intelligence who should succeed at almost anything he sets his mind to. The results may even understimate his IQ, especially in the verbal comprehension sphere, because of his delayed exposure to English and U.S. culture.

On the other hand, the fact that Billy’s English vocabulary is so high despite such delayed exposure to English is consistent with research showing the impotence of early childhood intervention. For a more extreme example, see The Case of Isabelle.

James Flynn writes:

…Current environment is surprisingly self-contained: it influences one’s current cognitive abilities with very little interference from past environments. Most of us assume that your early family environment leaves some sort of indelible mark on your intelligence throughout life. But the literature shows that this is simply not so.

From page 6 of Does Your Family Make You Smarter? by James Flynn.