(re-)Establishing the proximate cause

proponents of ethnic and racial differences in the past have been targets of censorship, violence, and comparisons to Nazis. Large swaths of the intellectual landscape have been reengineered to try to rule these hypotheses out a priori (race does not exist, intelligence does not exist, the mind is a blank slate…) Steven Pinker – The Edge Annual Question – 2006. “What is your dangerous idea?”

Reading through the literature on colorism has reminded me of a vexing problem. Quite a few people (in and outside of academia) seem to be 1) unaware of the phenotypic ethnoracial disparities in GMA, 2) unaware of the predictivity of GMA, 3) unaware of the biological basis of GMA, and 4) putting 1-3 together, unaware that these stubborn differences are the proximate causes of much socioeconomic disparity.

This ignorance has obviously been manufactured. And this makes it impossible to explain that the racial discrimination in the US is against Whites (and Asians) and for Blacks (and Hispanics).

The following points need to be established:
1) African Americans and Hispanic-Americans* are psychometrically “inferior”** to European Americans with respect to GMA
2) The above psychometric “inferiority” corresponds to a biological “inferiority.”
3) The above biological “inferiority” (genetically mediated or not) is the proximate cause of a substantial portion of the racial “disparity.”
4) The racial discrimination in the US is for African Americans and Hispanic-Americans (NAMS) and against White people and people deemed White enough.
5) 1-4 are indisputable. The empirical evidence is overwhelming.

* I no longer see any reason to qualify this with the phrases “on average” or “statistically speaking.” Leftists etc., purposely conflate the terms. Let them go out of their way to establish the distinctions.
**using leftist backed common parlance. Refer above.

To facilitate this, compendiums of readily citable articles need to be complied

A. Magnitude of the GMA gap (GMA = general mental ability*)

Roth et al., 2001. Ethnic group differences in cognitive ability and educational setting: A meta-analysis

Roth, Bobko, and Huffcut, 2003. Ethnic Group Differences in Measures of Job Performance: A New Meta-Analysis

Roth, et al., 2008. Work Samples tests in personal selection: A meta-analysis of Black-White differences in overall and exercise scores

Roth, 2010. Updating the trainability tests literature on black-white subgroup differences and reconsidering criterion-related validity.

Roth et al., 2011. TOWARD BETTER META-ANALYTIC MATRICES: HOW INPUT VALUES CAN AFFECT RESEARCH CONCLUSIONS IN HUMAN RESOURCE MANAGEMENT SIMULATIONS

Sackett and Shen, 2008. Subgroup differences on Cognitive tests in contests other than personal selection

B-W gap summary in standardized scores:
Overall job performance [d= .46,corrected]; GPA [d = .39]; Military and Industrial applicants [d = .6-1.1]; IQ/g [d= 1.2, adult]; GRE [d = .99]; LSAT [d = 1.23]; SAT [d = 1]; trainability [d = varying (e.g, IRS tech d = .8 -1.2; engineering assistant d = .4-.8 ]); work knowledge [d =.5]; differences in neuropsychiatric assessments [d = Varying (e.g BNT d = 1); visual spatial abilities [d = .5]; academic achievement tests [d = .6 – .8]; rates of Mild MR [d = .66, Florida]. Rates in crime [d = 1,between urban males Whitney (1990)].

B. Predictive validity of the GMA gap

Ones and Viswevaran, 2002. Introduction to the Special Issue: Role of General Mental Ability in Industrial, Work, and Organizational Psychology

Sackett, et al., 2008. High-Stakes Testing in Higher Education and Employment Appraising the Evidence for Validity and Fairness.

Schmidt and Hunter, 2004. General Mental Ability in the World of Work: Occupational Attainment and Job Performance

Kuncel and Hezlett, 2007. Standardized tests predict graduate students’ success

C. Biological basis of differences in GMA/g

Gottfredson, 2010. Intelligence and social inequality: Why the biological link?

Recent representative studies

Karama, et al., 2009. Positive association between cognitive ability and cortical thickness in a representative US sample of healthy 6 to 18 year-olds

Karama et al., 2011. Cortical thickness correlates of specific cognitive performance accounted for by the general factor of intelligence in healthy children aged 6 to 18

D. Attempts to get around the GMA gap

Sacket, et al, 2001. High-stakes testing in employment, credentialing, and higher education:
Prospects in a post-affirmative-action world

See: Strategies for Achieving Diversity Without Minority Preference

McDaniel, 2009. Gerrymandering in personnel selection: A review of practice

Ployhart, 2008. The diversity-validity Dilemma-Strategies for reducing racioenthic and sex subgroup differences and adverse impact in selection

Schmitt and Quinn, 2010. Reduction in Measured Subgroup Mean Differences: What is possible?

Notes

*In I-O, GMA (general mental ability) is often used instead of g (general intelligence.) Part of the reason is to avoid the manufactured controversy about general intelligence and to avoid nibbling criticisms.

Within populations, GMA gaps are equivalent to g gaps. Between populations, no psychometric method has been developed which can unequivocally prove that the GMA gaps are g gaps (i,e. prove Spearman’s hypothesis) Convergent evidence from neurology and industrial organization leave little doubt. Nonetheless, to circumvent criticisms, the gaps are often referred to as “g-loaded” (in the psychometric literature) or as being “GMA” gaps (in the I-O literature.)

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14 Responses to (re-)Establishing the proximate cause

  1. ggg says:

    Chuck, what do you make of the Fagan & Holland study? Egalitarians like to push this one around sometimes if they are extra knowledgable. I can’t find any criticisms of it.

    • JL says:

      IIRC Fagan and Holland gave a bunch of black and white students an IQ test, where the mean score for whites was found to be significantly higher. Then they gave the same students written material containing difficult/nonsensical word problems with answers, giving them time to memorize it all. Finally, they tested the students on those problems, and found that the two races scored equally well, i.e. there was no mean racial difference in ability to memorize this novel material.

      Fagan and Holland pointed out that vocabulary and verbal analogy problems are highly g-loaded, and argued that their experiments therefore prove that the black-white gap in IQ tests is an artifact of whites having had more previous exposure to the kind of material that the tests contain, and that blacks are not less intelligent than whites.

      What I think is actually going on in their experiments has to do what Arthur Jensen has called Level I and Level II abilities. Level I abilities are defined as “retention of input and rote memorization of simple facts and skills”, whereas Level II abilities are the same as g. Jensen found out that whites have a 1 SD advantage over blacks in g (Level II), but that there’s only a small white advantage in Level I abilities. Moreover, if you match whites and blacks for IQ (=Level II), the blacks will have better Level I abilities (Level I and II are correlated within races). See, for example, this paper.

      This suggests that the black students in Fagan and Holland’s study were indeed less intelligent than the white students (as indicated by IQ scores), but possessed as good rote-learning skills as the more intelligent white students. Jensen used to argue that rote-learning should be more widely utilized in black schools to reduce the achievement gap, but he has since abandoned this line of thinking, pointing out that scholastic achievement is all about g and memorization takes you only so far.

      It’s interesting that vocabulary tests are highly g-loaded even though just about anybody can learn the definitions of words if they are given the chance and motivation. For example, the 10-word WORDSUM test of the General Social Survey is highly correlated with IQ tests even though it takes only a few minutes to complete and has remained identical for decades. It seems that high-IQ individuals simply tend to seek out information more than those with lower IQs.

      • Chuck says:

        JL,

        Thanks for the comment. It puts my gangling one to shame. Also, thanks for the info on level I and level II racial differences. This makes for a quick, easy counter.

        SWPL: Fagan found…
        ggg: Level I and Level II abilities.
        SWPL: What?
        ggg: ….

      • JL says:

        I don’t think Jensen or anyone else uses the terms Level I and Level II anymore. The relative black advantage in Level I abilities is best seen as a black advantage in short-term memory. The forward digit span test is a classic test of short-term memory, and the b-w gap is quite small in it. This is how Phil Rushton put it:

        “On some sub-tests the Black-White difference is smaller and on other sub-tests the Black-White difference is larger. Black-White differences are markedly smaller on tests of rote learning and short term memory than on tests of reasoning and those requiring transformation of the input. For example, on the Forward Digit Span Test, in which people are asked to recall a series of digits in the same order as that in which they were presented, Black-White differences are quite small, but on the Backward Digit Span Test in which people recall a series of digits in the reverse order to that in which they were presented, they are quite large.”

      • Chuck says:

        JL,,

        I’m looking over Wicherts’ African IQ data. Wicherts states: “The full database includes 109 samples totaling 37,811 test-takers. The N-weighted mean of
        these studies is 76.5 (SD=6.7),” (in “The dangers of unsystematic selection methods and the representativeness of 46 samples of African test-takers”)

        In all the samples reported, the African SDs are lower than European SDs, For example, in “A systematic literature review of the average IQ of sub-Saharan Africans,” Wicherts notes:
        “Hence, the SD of IQ in African samples appears to be around 13 and sampling bias does not appear to be an issue in the current review.”

        Now, referring back to the average of 76.5, is this condition on a pooled standard deviation of 15? Obviously, if the African SD was 13 and the European SD was 15, the pooled SD would be 14 (assuming equally numerous people). A 23.5 point gap (based on different SDs) would then translate into 1.68 SD gap or 25 point gap on White metrics. I’m guessing that the adjustments have already been made — I was curious as to your opinion

      • JL says:

        Chuck, I haven’t looked at Wicherts’s African studies in detail, so I cannot really begin to guess.

        Apropos Wicherts, I’m looking forward to his meta-analysis of stereotype threat in African Americans. If his final conclusion is the same as the one he reported earlier, many people are not going to like it. It seems that his paper on this has been under review for a year now, which is a rather long time — I wonder if some editors/reviewers are giving him hell for it because such a meta-analysis could undermine the burgeoning “stereotype threat industry”, and the reputations of people like Claude Steele.

    • Chuck says:

      ggg,

      Thanks for bringing it to my attention. I’ll have to read it over….

      Based on my 5 minute scanning of his article, I would note the following:

      Here’s the crucial sections —

      “The g factor: Jensen (1998) assumes that IQ differences between African-Americans and Whites are due to differences in the g factor. Thus, Jensen would predict that the tests of general knowledge employed here, because they were solved equally well by AfricanAmericans and Whites, should have little, if any, relation to the g factor derived from standard IQ tests. In accordance with the manner in which Jensen (1998) derives g, estimates of g were obtained by performing a principle factor analysis (un-rotated) on the three types of IQ tests given in the third and fourth experiments in the present study and extracting the first principle factor in each case which accounted for 47% to 59% of the common variance from study to study….Moreover, and most importantly, none of the demographic variables, including, and in particular, race, played any significant role in the determination of g in either analysis. The theoretical import of these findings as to Jensen’s (1998) view that racial differences in IQ are due to differences in g will be discussed below”


      The findings of the present study, and those just noted, are interpretable on the basis of a theory of intelligence (Fagan, 1992, 2000) which assumes that the IQscore is a measure of knowledge, and that knowledge depends on information processing ability(intelligence) and on the information provided for processing”

      “opportunity for exposure to the information to be tested is assured”

      …………..

      Fagan appears to be arguing that the GMA (general mental ability) gap isn’t a biological-g gap (which he conceptualized as a “processing” gap). According to him, it’s an acquired knowledge gap — which masquerades as biological g-gap. This isn’t inherently implausible — which is why I included the note in my post: “In I-O, GMA (general mental ability) is often used instead of g …(refer above)

      Here are the problems I see with Fagan’s results:

      1) There’s a chronometric Black-White gap. For example, refer to: Pesta, Bryan J. and Poznanski, Peter J. (2008). “Black-White differences on IQ and grades: The mediating role of elementary cognitive tasks.” Intelligence. Vol 36, Issue 4, 323-329.

      While Fagan’s study might suggest a non-biological g-gap, the reaction time studies suggest otherwise. In evaluating a hypothesis you have to look at the totality of the evidence.

      2) There’s a neurological black-white gap. In ethnoracially representative studies Karama, et al., 2009. and Karama et al., 2011. found that (biological) g mediates the correlation between cortical thickness (not exactly a “cultural” or “knowledge” difference) and IQ, I haven’t got around to requesting the data (not that I would get it), but if the African-American and White IQ’s in those study were representative of the population (i.e if there was a black-white IQ gap between the subjects), this would clearly evidence Spearman’s hypothesis. If not, what?

      (The Ns for the above studies were small, but so were Fagan’s: “this conclusion is based on a sample of 925 participants (451 in the current study and 474 in the Fagan & Holland, 2002 study). The 925 participants include 620 White Americans and 305 African-Americans representative of the general US young adult population in terms of age and educational level”)

      3) The Black-White gap is g-loaded. Murray (2005) — Inequality taboo — comments on this:

      “A concrete example illustrates how Spearman’s hypothesis works. Two items in the Wechsler and Stanford-Binet IQ tests are known as “forward digit span” and “backward digit span.” In the forward version, the subject repeats a random sequence of one-digit numbers given by the examiner, starting with two digits and adding another with each iteration. The subject’s score is the number of digits that he can repeat without error on two consecutive trials. Digits-backward works exactly the same way except that the digits must be repeated in the opposite order.

      Digits-backward is much more g-loaded than digits-forward. Try it yourself and you will see why. Digits-forward is a straightforward matter of short-term memory. Digits-backward makes your brain work much harder.

      The black-white difference in digits-backward is about twice as large as the difference in digits-forward.[60] It is a clean example of an effect that resists cultural explanation. It cannot be explained by differential educational attainment, income, or any other socioeconomic factor. Parenting style is irrelevant. Reluctance to “act white” is irrelevant. Motivation is irrelevant. There is no way that any of these variables could systematically encourage black performance in digits-forward while depressing it in digits-backward in the same test at the same time with the same examiner in the same setting.”

      I’m straining my brain to see how that could be a function of accumulated knowledge.

      4) The Black what gap is greater on measures of performance IQ (Possessing speed, perceptual organization) than on measures of verbal IQ. If this was due to a “knowledge gap,” why would this be so? Moreover, there’s a spatial ability gap. That’s not knowledge in the ordinary sense.

      5) Most importantly, the Black-White gap is a GMA gap. And biological g is what allows for shared predictivity across tests. Here’s that in tables and graphs:

      The term GMA is more inclusive than one might think. It includes numerous dimensions not ordinarily defined as “knowledge.” (For example, work performance is not a form of knowledge (though it may require knowledge), nor is trainability, ditto simulation exercise performance (e.g here’s how to do X, now you do x)

      ……………………

      Now given these 5 points, what gives? How do we reconcile Fagan’s findings with the reality of differences in g. It’s worth looking at Fagan’s methodology.

      Fagan argues that the GMA differences don’t represent g differences (or, more specifically, processing differences). IQ test clearly show an IQ information processing difference. Let’s look at how Fagan is measuring “real” “processing.”

      Experiment 1.

      “They were also tested for their information processing ability by asking them to recognize 48 previously unfamiliar faces o which they had recently been exposed” “Nor is it new or surprising to find that information processing ability (indexed here by incidental recognition memory) is a significant predictor of knowledge”.

      Here Fagan is using facial memory as an alternative measure of processing speed (or g) — why not visual processing? While likely correlated with IQ, facial recognition and perhaps even memory, in general, is distinct from g.

      Experiment 2 +3 + 4

      “Some sayings were based on generally available information (e.g. “An apple a day keeps the doctor away” as meaning “Eating good food helps you to stay healthy”) others required past exposure to specific information (e.g. “Home of the bean and the cod” as meaning “Boston”). We assumed that AfricanAmericans and Whites, equally able to process information, would be equally able to comprehend the meanings of sayings based on generally available information but would differ in their comprehension of sayings requiring specific past information.”

      Here, Fagan is using knowledge of simple phrases as an alternative measure of processing speed (or g).

      Now, the findings are interesting, but why does Fagan interpret them as demonstrating no differences in g? I outline two (of many) possible interpretations:

      Fagan

      1. Tests of “commonly available knowledge” etc. are good measures of true processing (or g)
      2. In the study, tests of common knowledge etc are correlated with IQ (g) within both races.
      3. Whites had superior IQ as measured by PPVTR.
      3. Whites did not do superior on tests of common knowledge etc.

      Ergo. The superior white IQ does not represent a superiority in IQ (g), but merely represents a white uncommon knowledge advantage. (They have more exposure to complex things)

      Chuck

      1. The superior white IQ represents a superiority in IQ (g)
      2. In the study, tests of “commonly available knowledge” etc correlated with IQ (g) within both races.
      3. Whites had superior IQ as measured by PPVTR.
      3. Whites did not do superior on tests of common knowledge etc.

      .Ergo. Tests of commonly available knowledge are not good measure of true processing (or g), but merely represent interesting correlates of it. As a tentative hypothesis for the lack of racial gap in commonly available knowledge, etc: Blacks have a common knowledge advantage. (They have more exposure to simple things).

      I’ll try to think of a way to test this.

    • Chuck says:

      Ok,

      I thought about Fagan some more. Here’s the biggest problem that I see. (Jensen’s critique developed here):

      The within population heritability of IQ for African Americans is the same as it is for Whites. By adulthood, the h^2 approaches .80. Moreover, the .20 environmental variance is split into between family variance and within family variance (let’s say .1 and .1). Differences between whites and blacks with regards to “knowledge” exposure is a form of between family variance.

      Now, it follows that differences in IQ between blacks are not significantly caused by differences in exposure to knowledge (otherwise the between family environmental variance would be much higher). For the 1.1 SD adult black-white gap (as reported by Flynn) to be caused by differences in knowledge exposure between black and white families):

      either 1) there would have to be a 3.5 SD knowledge gap (e^2 =1; 1.1/sqrt .1 = 3.5). If so, African American would have to be exposed to the equivalent of the white .023:

      or 2) the 1.1 SD “knowledge” gap would have to be an x-factor. Some factor which uniformly effects the Black and white populations (i.e. every member equally). Now, my White Privileged Magazine subscription ran out a while ago — so I’m no longer getting my 1.1SD insider knowledge. What about yours?

  2. Chuck says:

    Apologies for grammar/ spelling. It’s late.

  3. Chuck says:

    So what would be our quick rebuttal? It’s important to have those on hand.

  4. nikcrit says:

    “3) The Black-White gap is g-loaded. Murray (2005) — Inequality taboo — comments on this:
    “A concrete example illustrates how Spearman’s hypothesis works. Two items in the Wechsler and Stanford-Binet IQ tests are known as “forward digit span” and “backward digit span.” In the forward version, the subject repeats a random sequence of one-digit numbers given by the examiner, starting with two digits and adding another with each iteration. The subject’s score is the number of digits that he can repeat without error on two consecutive trials. Digits-backward works exactly the same way except that the digits must be repeated in the opposite order.
    Digits-backward is much more g-loaded than digits-forward. Try it yourself and you will see why. Digits-forward is a straightforward matter of short-term memory. Digits-backward makes your brain work much harder.
    The black-white difference in digits-backward is about twice as large as the difference in digits-forward.[60] It is a clean example of an effect that resists cultural explanation. It cannot be explained by differential educational attainment, income, or any other socioeconomic factor. Parenting style is irrelevant. Reluctance to “act white” is irrelevant. Motivation is irrelevant. There is no way that any of these variables could systematically encourage black performance in digits-forward while depressing it in digits-backward in the same test at the same time with the same examiner in the same setting.”
    I’m straining my brain to see how that could be a function of accumulated knowledge.”

    OK, I’d like to add a observation here, though it’s quite qualitative and somewhat anecdotal standing beside all these other remarks of late; I’d also like to somewhat qualifiy my forthcoming comment by saying in no way am I confidently disagreeing with anything specific here; rather, i’m quite sure that many of my background and orientation-level regarding hard quantified social-science data very likely have some of the questions that i now advance.

    Re. the segment of the IQ test that asks for recitations of multi-digited numbers —— first, ‘frontwards,’ then ‘backwards’, with the stated agreement that the latter task is much harder a mental task, which is much more ‘g-loaded’, while the digits-forward exercise requires mere ‘short-term memory.’ the conclusion to this segment above states that the different results between black and white testtakers, witth whites doing twice as well on digits-backward recall is proven and ‘clearly not the result of cultural difference,’ or words to that effect.
    Ok. In my job, I notice and have noticed for years, the much casually discussed about how african-americans are more of a ‘oral culture,’ while white/euro society are more literal, concrete, etc.; now, i know how this sounds, and again, i’m putting it forth merely as good-faith curiosity, but I can clearly image bunches of urban black children that i see quite regularly, reciiting the digits-forward requests aloud, turning them into little rhythmic jingles, more or less taking the stated words and working them into some sort of impromptu choreography while stamping their foot or tapping the table or even reciting them in a rhythmic sing-song like way, etc.; by my lights, black kids do this much more often in general, evident in learning tasks, coping situations, as momentary episodes of social engagement, etc., much moreso than do white children of comparable age and background, etc.
    So, when it comes to the digits-backward task, that relative advantage or cultural-mode of ‘oral conversion’ if you will is suddenly of no import at all; and here the literal or concrete hearing-retaining-and-repeating mode of literal transference, typical of written-language cultures, would seem to be advantageous.

    Now, is one mode better than the other, even if it was proven to be quite racially or ethnically consistent? Don’t know; and i don’t really care for hte sake of what i’m trying to convey here; but my point is that what i propose as a possible factor here IS clearly cultural. I guess what i’m wondering is, how can quantifiable social science ever even come close to ‘controlling’ for stuff like that? How can empriical observation and data NOT be somewhat ineffable always when trying to gauge social experience?

    (for the record, I clearly think something is there on the side of hereditarian causation —– but I really think ‘proving’ as much is, if not exactly beside the point, woefully lacking in claiming to be the ‘solution.’ Such proof was widely accepted at the turn of the 20th-century, though now of course disregarded. and i can’t help but wonder if all the current forms of proof won’t also eventually simply become ‘the new phrenology.’
    I agree with the hbd’ers that the consistent social stratification between the races is proof that hbd is somehwat true —– if you choose that paradigm; the so-called ‘anti-racists’ aren’t so much denying the hard science (at least not consistently); they’re more or less attacking their ideological opponents with a qualitative arsenal, more or less accusing it of a crisis of spirit and imagination.

    • Chuck says:

      “Now, is one mode better than the other, even if it was proven to be quite racially or ethnically consistent? Don’t know; and i don’t really care for hte sake of what i’m trying to convey here; but my point is that what i propose as a possible factor here IS clearly cultural. I guess what i’m wondering is, how can quantifiable social science ever even come close to ‘controlling’ for stuff like that?”

      When black and Yellow people are matched using IQ correlated variables they perform the same. For example, within both the back and yellow populations, IQ correlates with education and other variables. If you match members for education and other variables, you will find no digit sum gap — even though there is still, presumably, a cultural gap.

      The larger issue is the predictivity of the differences. Read through the linked paper: Sackett, et al., 2008. High-Stakes Testing in Higher Education and Employment Appraising the Evidence for Validity and Fairness.

      If the digit sum difference was do to “culture,” that same culture would have to account for the whole manifold of social, educational, psychological, etc., differences (if it didn’t, digit sum ability wouldn’t be predictive right?). All those differences are related — to varying degrees — by a common factor. In other words, this common factor is the PROXIMATE cause of many differences. Now, what’s the ultimate cause? I guess it could be that culture — but we have that complex argument which suggests culture isn’t the complete explanation.

      Notice, I never say that that gap is all or mostly due to this or that — I don’t need to. Small differences can have large effects in competitive markets. When Nickrit and Joe sixpack are applying for job, it’s the marginal difference that counts.

  5. JL says:

    What do they actually mean by “commonly available words”? Did they make the meanings of those words available to the students before testing, or did they just assume that some words are commonly available while others aren’t? If the latter, how did they decide which words are commonly available? Are commonly available words simply those easy words that just about everybody knows, or what?

    I am also puzzled by the choice of facial recognition as a test of information processing ability, because facial recognition has long been known as the rare mental ability that is not correlated with IQ (this can easily be seen in the fact that infants are pretty good at recognizing faces even though they are dumb as rock).

    Had Fagan and Holland really wanted to test if whites and blacks are equal in intelligence, they should have given those students something more difficult to learn, instead of testing them on something that can be easily memorized. From studies on the predictive validity of the SAT we of course know that SAT scores do not underpredict black performance in college even though whites and blacks attend the same courses and read the same textbooks, i.e. information is equally available to both races.

  6. JL says:

    I just read Fagan and Holland’s 2002 article “Equal opportunity and racial differences in IQ”. It describes a series of experiments similar to those in their 2007 paper, but in the 2002 paper they explicitly say that the test subjects were given opportunity learn the words to be tested before each testing situation. The results showed that there was no difference between whites and blacks in ability to learn new word meanings, even though the former had a significantly higher mean IQ.

    Both papers are, quite explicitly, attacks on Arthur Jensen’s theory of racial differences in mental ability. Therefore, it’s strange that there is not a word on Jensen’s research on the difference between memorization (Level I) and g (Level II) in either paper.

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