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).

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.

Imagine a pushy mother really wants her average 9.5-year-old son to get into a gifted class. Because IQ tests are normed for age and her son looks young for his age, she decides to tell the psychologist he’s only 6.5, so that he will get a much higher score.

Now assuming the boy is average for a 9.5-year-old in all cognitive domains he should score an age-ratio IQ of 146 in all domains, if the psychologist believes he’s 6.5 (because 9.5 is 146% of 6.5), however modern IQ tests use the deviation scale, where scores are assigned not by how many years advanced a kid is, but by one’s rank, relative to other American kids in one’s own age group. Being in the top 99% gives one an IQ of 65, being in the top 90% gives one an IQ of 80, being in the top 50% gives one an IQ of 100, being in the top 10% gives one an IQ of 120, and being in the top 1% gives one an IQ of 135, and being in the top 0.1% gives one an IQ of 146 etc.

Now obviously the average 9.5-year-old pretending to be a 6.5-year-old will get a high IQ in every domain, but his margin of superiority varies dramatically depending on the test. If he taken the WISC-R for example (before the norms expired), here’s how he’d have scored (for the readers convenience, I converted subtest scores, normally scaled from 1 to 19 into IQ equivalents):

Now after adjusting for test reliability, our gifted 6.5-year-old (who is secretly an average 9.5-year-old) had deviation IQs ranging from 117 (object assembly) to 145 (Arithmetic).

Why such a huge discrepancy? The most obvious answer is that 9.5-year-olds have two cognitive advantages over 6.5-year-olds. Not only are their brains bigger and more developed, but they’ve also have three extra years of life experience. On tests that require novel problem solving, their advantage will be modest because it only reflects their neurological superiority. It can not reflect their life experience advantage because by definition, novel problems are things we’ve had little experience with.

By contrast, on tests that required acquired knowledge they have two advantages. Not only does the 9.5-year-old have more neurological ability to reason arithmetically, learn and remember facts, and infer the meaning of words, but he’s also had three extra years to acquire number concepts, general knowledge, and vocabulary. Because “crystallized” tests require both neurolgical ability and experience, they show a much steeper age progression than fluid tests (and a much steeper decline in old age, though this is confounded with the Flynn effect), which require only neurological ability (beyond some basic experience threshold that virtually all Americans reach by age 5 or so). Indeed looking at the age progression is a good way to quantify crystalized vs fluid.

Notice also that the tests that show the biggest age effects also tend to be the ones that show the biggest family effects per James Flynn’s method. Because both reflect experience.

Now let’s imagine when the pseudo-gifted boy turned 16.83 and he wanted to get into Mensa, and they were unwilling to accept scores from the past. He is still exactly average in all domains for his true age, but still looking young he tells the psychologist he is only 10.5. She doesn’t buy it, but she’s not about to turn down $800 for a few hours work so she plays along.

Here are his results:

Once again, his years of extra life experience (relative to the age group he’s pretending to be) gave him a huge advantage on knowledge based tests like Vocabulary and Information. And once again, novel tasks like Block Design, Picture Arrangement, Mazes and Digit Span showed less advantage.

But what happened to Arithmetic? His advanced age gave him a huge advantage when he was a 9.5-year-old pretending to be 6.5, but now that he is 16.83 pretending to be 10.5, this subtest is even less age dependent than Block Design. The likely explanation is that once kids acquire basic number concepts in school (addition, subtraction, multiplication, and division) arithmetic depends less on experience and more on neurology.

This is why one can never say, categorically, that a given test measures fluid or crystallized ability. It depends on the population taking it. For example the Raven progressive matrices might be a fluid test within generations but a crystallized test between generations. Even something as seemingly crystallized as the math SAT might measure fluid ability in 17-year-olds with at least four years of advanced math. Among all 17-year-olds, it will still correlate with (but not so much be directly caused by) fluid ability because those with more fluid ability are likely to take advanced math in the first place.

Another interesting case is Similarities, which requires one to infer the link between common things (how are chess and scrabble alike?). This showed small age effects in early childhood, but large age effects in later childhood. At the lower end this test is just about the ability to see associations, but at the higher end, it becomes increasingly dependent on diction and sometimes esoteric concepts, making it more experience dependent.

One question is why, if crystallized tests are more culture dependent, do they often load more on psychometic g (the general factor of IQ tests believed to be a property of the physical brain). Perhaps as some have suggested, once you control for age, in countries where everyone has opportunity for schooling, knowledge tests measure both the ability to learn over an entire lifetime and the ability to store and retrieve a lifetime of learning. By contrast fluid tests only measure the ability to learn in the testing room, and not the ability to store and retrieve it years later. One theory is the more parts of the brain a test samples, the more g loaded it is, which would make sense if g is just overall cognition.

Loved ones keep begging to go out for a walk and get some fresh air. They say it’s not good for me to be hiding in the house all day and that I need exposure to the sun. I went for a half hour walk yesterday but spent most of my time on the road because I didn’t want to pass other humans on the sidewalk. But even when no one else is around, I’m still not sure if it’s safe to walk. What if this virus stays in the air just waiting for someone to walk through it?

This whole thing could have been minimized if we had just stopped international travel a few weeks earlier. Virtually every case in my city was brought here by someone traveling abroad.

I wonder if our failure to contain this thing is evidence of dysgenics?

It’s during times like this we see who are the truly intelligent. It’s the people who can adapt the situation to our advantage by making masks, test kits, ventilators, developing vaccines, and pushing common sense public policy.

The great writers, artists and philosophers may think they’re the most intelligent, but they’re not the ones who can save us.