Short answer: that isn't done. At all!
Which test does the military use?
a) The number of persons originally enlisted or inducted to serve on active duty (other than active duty for training) in any armed force during any fiscal year whose score on the Armed Forces Qualification Test is at or above the tenth percentile and below the thirty-first percentile may not exceed 20 percent of the total number of persons originally enlisted or inducted to serve on active duty (other than active duty for training) in such armed force during such fiscal year.
b) (b) A person who is not a high school graduate may not be accepted for enlistment in the armed forces unless the score of that person on the Armed Forces Qualification Test is at or above the thirty-first percentile; however, a person may not be denied enlistment in the armed forces solely because of his not having a high school diploma if his enlistment is needed to meet established strength requirements.
–– 10 U.S. Code § 520. Limitation on enlistment and induction of persons whose score on the Armed Forces Qualification Test is below a prescribed level
Does this talk about an 'IQ'-test?
"Armed forces" currently say this themselves:
To join the Army as an enlisted member you must usually take the Armed Services Vocational Aptitude Battery (ASVAB) test and get a good score. The maximum ASVAB score is 99. For enlistment into the Army you must get a minimum ASVAB score of 31.
–– ASVAB Scores and Army Jobs
What is the ASVAB?
A test that's widely used, and the resulting
An Armed Forces Qualification Test (AFQT) score is used to determine basic qualification for enlistment.
And that one does correlate somewhat
The AFQT is not individually administered but is one of the most highly g-loaded tests in use (g refers to the general intelligence factor). It correlates with the classic IQ tests more highly than they do with one another (Herrnstein and Murray, 1994, pp. 580-585). The g measured by the AFQT is skewed toward crystallized g (the tools and skills that intelligent people tend to acquire), but the same is true of the Wechsler tests (Jensen, 1987, p. 96).
More specifically, even though AVASB and WAIS are said to measure 'the same thing', a small subset that is, and are said 'to correlate highly' on that, this correlation is what?:
The correlation between AFQT and WAIS was 0.80 for white airmen and 0.77 for black airmen. These sugnificant positive relationships indicate that AFQT and WAIS are measuring basically the same factor.
(src: Office of the Secretary of Defence: "Relationship between AFQT and IQ – Inclusion for ASVAB Back-Up Book", 4 September 1980 PDF)
The whole army procedure is not an IQ test. IQ test measures how good one is at taking IQ tests, and the army test is similar in that circularity.
It is not sound science to 'calculate from any AFQT score an equivalent IQ'
William J. Matthews writes that part of The Bell Curve's analysis is based on the AFQT "which is not an IQ test but designed to predict performance of certain criterion variables". The AFQT covers subjects such as trigonometry.
Heckman observed that the AFQT was designed only to predict success in military training schools and that most of these tests appear to be achievement tests rather than ability tests, measuring factual knowledge and not pure ability. He continues:
Ironically, the authors delete from their composite AFQT score a timed test of numerical operations because it is not highly correlated with the other tests. Yet it is well known that in the data they use, this subtest is the single best predictor of earnings of all the AFQT test components. The fact that many of the subtests are only weakly correlated with each other, and that the best predictor of earnings is only weakly correlated with their "g-loaded" score, only heightens doubts that a single-ability model is a satisfactory description of human intelligence. It also drives home the point that the "g-loading" so strongly emphasized by Murray and Herrnstein measures only agreement among tests—not predictive power for socioeconomic outcomes. By the same token, one could also argue that the authors have biased their empirical analysis against the conclusions they obtain by disregarding the test with the greatest predictive power.22
Janet Currie and Duncan Thomas presented evidence suggesting AFQT scores are likely better markers for family background than "intelligence" in a 1999 study:
Herrnstein and Murray report that conditional on maternal "intelligence" (AFQT scores), child test scores are little affected by variations in socio-economic status. Using the same data, we demonstrate their finding is very fragile.
–– Criticism of use of AFQT
What is g-factor?
the g factor targets a particular measure of general intelligence. […]
The g factor typically accounts for 40 to 50 percent of the between-individual performance differences on a given cognitive test, and composite scores ("IQ scores") based on many tests are frequently regarded as estimates of individuals' standing on the g factor.
–– Kamphaus, R.W., Winsor, A.P., Rowe, E.W., & Kim, S.: "A history of intelligence test interpretation", in: D.P. Flanagan and P.L. Harrison (Eds.), "Contemporary intellectual assessment: Theories, tests, and issues" (pp. 23–38). New York: Guilford, 22005.
In other words: A poorly operationalised construct, apparently even a poorly operationalisable construct, that is somehwat elusive, but certainly not properly measured with any one IQ-test
–– H.-M. Süß: "The construct validity of the Berlin Intelligence Structure Model (BIS)", in: A. Roazzi, B. Campello, W. Bilsky (Ed): "Proceedings of the 14th Facet Theory Conference. Searching for structure in complex social, cultural & psychological phenomena", Facet Theory Organization, Recife, Brazil 2013.
We see that the military uses one test that claims to 'measure' an estimate of less than 50% of any persons cognitive abilities.
Any 'IQ' is a different wobbly rubber stick and AFQT is yet another one, used to 'measure' a different set of skills.
The IQ concept was valuable, even sophisticated –– for 1916. But it proved to be a rubber yardstick.
Second, the two main theoretical approaches featured in this chapter—neuropsychological processing and CHC—are two among many theories of intelligence. I am well aware that some of the most popular and ingenious theories, notably Sternberg’s (1988b, 1999) triarchic theory of successful intelligence and Gardner’s (1993) multiple-intelligence theory, are far more comprehensive and encompass many more abilities than the handful of theories that have formed the foundation of modern IQ tests.
As Sternberg (1988b) has said for years, IQ tests measure only one of the three prongs of his theory—analytic abilities, but not practical intelligence or creativity. (He is correct.) From the perspective of Gardner’s eight multiple intelligences, IQ tests assess only three: linguistic, logical-mathematical, and spatial (Chen and Gardner, 2005, give credit only for the first two, but IQ tests have measured spatial intelligence for 70 years). No question, though, IQ tests do not measure Gardner’s other five intelligences, many of which are noncognitive: musical, bodily-kinesthetic, naturalistic, interpersonal, and intrapersonal (i.e., self-insight).
Two decades ago, Sternberg (1988a) said, “Intelligence tests of the present are anachronisms” (p. 8), and Gardner (1988) said, “The whole concept [of IQ tests] has to be challenged; in fact, it has to be replaced”
My own view? The existing IQ tests, simply by following their own theoretical approach to what intelligence is, are immediately wrong or invalid from boxloads of other, sometimes opposite, viewpoints.
–– "History Part 2: At long last, theory meets practice" in: Alan S. Kaufman: "IQ testing 101", Springer: New York, 2009.
Nassim Nicholas Taleb:
“IQ” is a stale test meant to measure mental capacity but in fact mostly measures extreme unintelligence (learning difficulties), as well as, to a lesser extent (with a lot of noise), a form of intelligence, stripped of 2nd order effects — how good someone is at taking some type of exams designed by unsophisticated nerds. It is via negativa not via positiva. Designed for learning disabilities, and given that it is not too needed there (see argument further down), it ends up selecting for exam-takers, paper shufflers, obedient IYIs (intellectuals yet idiots), ill adapted for “real life”. (The fact that it correlates with general incompetence makes the overall correlation look high, even when it is random, see Figures 1 and 2.) The concept is poorly thought out mathematically by the field (commits a severe flaw in correlation under fat tails and asymmetries; fails to properly deal with dimensionality; treats the mind as an instrument not a complex system), and seems to be promoted by
Racists/eugenists, people bent on showing that some populations have inferior mental abilities based on IQ test=intelligence; those have been upset with me for suddenly robbing them of a “scientific” tool, as evidenced by the bitter reactions to the initial post on twitter/smear campaigns by such mountebanks as Charles Murray.
Psychometrics peddlers looking for suckers (military, large corporations) buying the “this is the best measure in psychology” argument when it is not even technically a measure — it explains at best between 2 and 13% of the performance in some tasks (those tasks that are similar to the test itself)[see interpretation of .5 correlation further down], minus the data massaging and statistical cherrypicking by psychologists; it doesn’t satisfy the monotonicity and transitivity required to have a measure (at best it is a concave measure). No measure that fails 80–95% of the time should be part of “science” (nor should psychology — owing to its sinister track record — be part of science (rather scientism), but that’s another discussion).
IQ is largely a pseudoscientific swindle, 2018
That's for all means and purposes a pity.
On the one side we see poor statistics, outright fraud, even in contrast to those who construct psychometrics themselves for a profession, but know the limitations. On the other side we see the right-wingers, racists, eugenicists, antisemites who basically claim that "this time we did phrenology right"
… it turns out that he, a professor of psychology, doesn’t understand how the brain works.
To fully grasp the depth of Peterson’s belief in power hierarchies, take his commitment to IQ testing: “If you don’t buy IQ research,” he has told his students, “then you might as well throw away all of psychology.” Peterson rejects the theory of multiple intelligences (emotional intelligence, musical intelligence, and so on) and insists that all of human intelligence is biologically determined, essentially unalterable, and expressed in a single number that can be ranked. Your IQ, he says, will govern where you end up in life: with an IQ of 130, you can be an attorney or an editor; at 115, you can be a nurse or a sales manager; at 100, you can be a receptionist or a police officer; at 90, you can be a janitor.
Peterson’s defence of IQ rests on shaky foundations. While he tells students that IQ was empirically established through Charles Spearman’s factor analysis, he does not share the well-known critique of that method: factor analysis supports both of the contradictory causal explanations of intelligence (intelligence as innate versus intelligence as the product of environmental advantage). Peterson then stacks the deck in favour of biology, citing brain size and neural conduction velocity (essentially, the speed at which an electrical pulse moves through tissue) as the determinants of IQ. Again, he does not tell students that both explanations were discredited by later research.
In the tradition of nineteenth-and early twentieth-century pseudo-scientists, phrenologists, quacks, and scientific racists, Peterson’s commitment to IQ is simply the reflection of his commitment to an unalterable hierarchy of human beings. And this is why his dismissal of “unnatural” and “made up” gender pronouns, alongside his casual sexism—his belief that women would be better served by having babies than careers and that male feminists are “creepy”—turns out to be central to his intellectual project, which seeks to resurrect the conventional patriarchal pecking order. For Peterson, transgender people and powerful women upset the “male dominance hierarchy” that forms the centerpiece of his thought. His world view is predicated on the promise of restoring authority to those who feel disempowered by the globalism, feminism, and social-justice movements he derides.
I have to object to the phrase “stacks the deck in favour of biology”, because no sensible biologist would accept that load of crap as in any way valid. It is not good that “the most famous professor in Canada”, as the article calls him, is promoting bad science.
PZ Myers: "Jordan Peterson is peddling IQ myths and fallacies", Pharyngula, 29 November 2017
Peterson goes on that the military would have conducted 'internal studies' to determine that anyone below 83 would "absolutely positiveley counterproductive". Well, he seems to want to have a talk with people in occupations like 'police'?
"So you’ve learned you’ve got a “pitifully” low IQ. How worried should you be?"
In reality, the military would accept people that if they should score "IQ 84" that would represent this: a 'high risk' for any kind of promotion?
- Discount candidates scoring in a high-risk zone but be prepared to check the risk against alternative measures.
- Be very cautious with the high/medium risks and cautious with the medium risks relative to the demands of the role.
- Wherever possible, check whether a combination of upper-decile extraversion and lower-decile agreeableness has led to a reputation for combative or provocative behaviour, or lower-decile agreeableness combined with lower-decile conscientiousness has left a reputation for inconsiderate or unruly behaviour.
- Total the values achieved against the factors and favour the highest-scoring candidate.
–– Barry Cripps: "Psychometric Testing. Critical Perspectives", Wiley: Chichester, 2017.
Q How accurate are his specific claims?
They are made up. Wrong on every level that isn't extremely trivial.
Q The US military uses IQ testing to determine potential recruits' cognitive abilities.
They do not. Since 1976 they use a different discrimination instrument.
Q the military forbids anyone with an IQ under 83 from joining.
No again. They usually decline people scoring too low in the test they use. That isn't fixed, but flexible and subject to change and there are exceptions even now. Statistically and scientifically the claim Peterson presents makes no sense and he abuses it. Not least in using an illusory precision of 83 when even the non-allowable equivalence would be ~81.
Q because their experience has shown that anyone with an IQ under 83 will be more of a liability than an asset to the military.
Unfounded claim, unrelated to any IQ. What he wants to say is that the military tries to avoid recruiting the dumbest of the dumb. Trivial. But the number 83 and IQ are no where to be found. He makes a strong claim and is unable to back it up. In short: this looks like a primitive lie .
Perhaps this might help the detractors. While the transfer calculation between two supposedly highly correlated tests is not "easily done" or even correct, they might as well be compared:
IQ scores for Blacks across three decades (White average 5 100). Results are shown for the Armed Forces Qualification Test (AFQT), the Stanford-Binet (SB), the Wechsler Adult Intelligence Scale (WAIS), and the Wechsler Intelligence Scale for Children (WISC). For the WAIS, mean scores for all ages (16–74) are indicated by the dashed line, and mean scores for individuals under age 25 are indicated by the solid line.
–– William T. Dickens & James R. Flynn: "Black Americans Reduce the Racial IQ Gap. Evidence From Standardization Samples", Psychological Science, Volume 17—Number 10, 2006.
Homework question: Were 50% of all black recruits dismissed until 1987?
A simple math equation may be allowed. Even though the calculation isn't overly meaningful. If you still assume that 'IQ'=intelligence, convertible between test measuring different things that are merely correlated (remeber that AFQT is not an IQ test):
The 31st percentile returns an IQ of 93; the 10th percentile is an IQ of 81.
Going back to "the law":
Translating from percentiles to 'IQ', the law implies that an IQ below 81 (“tenth percentile”) is disqualifying, and dictates that persons with IQ’s between 81 and 93 (“thirty-first percentile”) cannot comprise more than 20% of all enlistees.
–– (src, comparison)
For added redundancy:
We do not find such a pattern. Table 8.2 lists the ASVAB weights for the first principal component; these weights suggest that while AFQT is highly correlated with g (P = 0.829), it is a suboptimal measure of general intelligence, which suggests that H&M may underestimate the effect of intelligence on social outcomes.
Our results are consistent with the theory of general intelligence: our version of g explains a high proportion of the variance in test scores and g is remarkably similar across race and gender. However, our results conflict with the predictions of H&M. Ability factors other than g are economically useful. Compared with education, family background, and region of residence, g explains little of the variance in wages; if there exists some "X factor" that can explain the large residuals common in wage regressions, it is not measured cognitive ability.
We also find that the returns to g differ significandy across race and gender; payment is not made for "ability" alone, which violates the definition of meritocracy advanced by H&M. In summary, our reanalyses of the NLSY data originally analyzed by H&M show measured cognitive ability is correlated with wages but explains little of the variance in wages across individuals and time. This finding is mirrored in Ecclesiastes 9:II:
… [f]he race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favor to men of skill; but time and chance happeneth to them all.
–– Cawley: "Cognitive Ability, Wages, and Meritocracy", in: Bernie Devlin et al (Eds): "Intelligence, Genes, and Success. Scientists Respond to The Bell Curve", Springer: New York, 1997. (Herrnstein and Murray use the Armed Forces Qualifying Test (AFQT), an equally weighted composite of four items of the ASVAB, as their measure of IQ. They show that the AFQT has the internal structure of an IQ test and that it correlates highly with traditional IQ tests. They further argue that it is one of the best measures of general intelligence or g currently available. (See, however, the chapter byJohn Cawley et al. in this volume, in which they argue that the AFQT is a flawed measure ofgeneral intelligence.))
At least the military says to Peterson:
Efforts are being made by military behavioral science research programs to develop additional screening instruments, including measures that supplement the predictive power of the high school diploma and AFQT score. Such endeavors might result in small gains to expand the recruitment pool and reduce attrition. Even with increased quotients of those who have graduated from high school and who had appropriate AFQT scores, first-term attrition remains more than 30%.
There is not an inexpensive screening tool with adequate predictive validity and reliability to identify individuals at high-risk of attrition before they enter military training and service. The best predictor of success in the military is still a high school diploma or 2 or more years of college.
Robert Cardona & Elspeth Cameron Ritchie: "Psychological Screening Of Recruits Prior To Accession In The US Military" (PDF)