Monday 7 March 2016

Tilting at racial difference

I had not come across the notion of “tilt” when discussing the pattern of verbal/performance discrepancies before, but it captures the main finding well: most of us tilt in one direction or another towards maths or verbal  abilities (Counting or Chattering), with considerable impact on our working lives. A paper on sex differences in “tilt” by Coyle, Richmond and Snyder was presented at the Albuquerque conference last year.

Now here is a published paper from Coyle on the pattern of abilities in Africans and Europeans.

Thomas R. Coyle. Ability tilt for whites and blacks: Support for differentiation and investment theories  Intelligence, Volume 56, May–June 2016, Pages 28–34 doi:10.1016/j.intell.2016.02.002

What does Thomas Coyle say?

This research is the first to examine race differences in ability tilt for whites and blacks, two groups that show an average difference in g (favoring whites) of about one standard deviation. Tilt was defined as within-subject differences in math and verbal scores on three aptitude tests (SAT, ACT, PSAT). These differences yielded math tilt (math > verbal) and verbal tilt (verbal > math), which were correlated with specific abilities (verbal and math) and college majors in STEM (science, technology, engineering, math) and the humanities. Math tilt was higher for whites than blacks, whereas verbal tilt was similar for both groups. In addition, tilt correlated positively with similar majors and abilities (e.g., math tilt and math ability), and negatively with competing majors and abilities (e.g., math tilt and verbal ability). Tilt effects were generally stronger for whites, and were unrelated to g. The results support differentiation theories, which predict higher levels of tilt for higher ability subjects, and investment theories, which predict negative tilt effects for competing abilities (e.g., math tilt and verbal ability).

This research examines race differences in ability tilt (hereafter tilt) for whites and blacks. Tilt refers to within-subject differences in math and verbal scores on aptitude tests such as the SAT (formerly, Scholastic Aptitude Test) and ACT (formerly, American College Test). The SAT and ACT are college admissions tests, and are strongly related to IQ and general intelligence (g), the variance common to mental tests (e.g., Coyle and Pillow, 2008 and Frey and Detterman, 2004). The SAT and ACT yield two types of tilt: math tilt (math > verbal), which indicates math strength, and verbal tilt (verbal > math), which indicates verbal strength. Both types of tilt are unrelated to g, but still predict later achievements (e.g., academic performance and college majors). The predictive power of tilt is surprising, because non-g factors generally have little predictive power ( Coyle, 2014).

Math tilt predicted achievements in science, technology, engineering, and math (STEM) (e.g., patents, math degrees). In contrast, verbal tilt predicted achievements in the humanities (e.g., novels, English degrees).

Whites and blacks show an average difference in g (based on g-loaded tests) of about one standard deviation, with whites being the higher ability group ( Rushton & Jensen, 2005; see also, Coyle, Purcell, & Snyder, 2013). This white–black difference in g may be related to tilt, a possibility predicted by differentiation theories (Deary et al., 1996; see also, Garrett, 1946 and Woodley, 2011). Differentiation theories predict that mental abilities become more differentiated (and less g loaded) at higher levels of ability. This differentiation is assumed to reflect cognitive specialization, which increases the effects of specific abilities. If tilt reflects specific abilities (math or verbal), it follows that tilt levels and effects may be higher for whites, the higher ability group.

Test scores were drawn from the 1997 NLSY, a representative sample of U.S. youth born between 1980 and 1984 (N = 8984). Following Coyle et al., 2014 and Coyle et al., 2015, subjects were selected if they had ASVAB scores and SAT or ACT scores. The race and ethnicity codes of the NLSY determined classification as white (white race and non-black/non-Hispanic ethnicity) or black (black race and black ethnicity). The final sample consisted of 1281 whites (593 males) and 378 blacks (146 males). College majors in STEM or the humanities were available for 252 whites and 58 blacks.

Following prior research (Coyle et al., 2014 and Coyle et al., 2015; see also, Park et al., 2007), tilt scores were computed by standardizing subtest scores and taking the within-subject difference (math − verbal) between math and verbal scores. Because the math and verbal scores of each subject differed after being standardized, all subjects showed some degree of tilt.




So, here are some statistics I can understand. What strikes you about black/white difference, the subject of this paper? If you look at analysis 3 which gets us closer to the raw data, sure there is a 1 standard deviation difference in means, which could be there for any number of reasons. However, the black standard deviation is smaller than the white standard deviation.  On SAT maths the black dispersion of scores is 18% less than the white, on SAT verbal 8% less; on ACT maths 31% less, on ACT  verbal 13% less; on PSAT maths 9% less and on PSAT verbal 2% less. Although the tests differ in the extent of the effect, all find the black dispersion of scores more narrow and constrained than the white, and the effect is stronger for the maths tests than verbal tests.

I digress, but all the animus about racial differences in intelligence seems to evaporate the moment the discussion moves from Means to Standard Deviations. Curious. When discussing Means there is nothing much, a priori, to distinguish between genetic and environmental causes of mean differences. It could be genetic transmission of ability, it might also be the circumstances in which people grow up and live. However, when it comes to Standard Deviations, in my view the environmental explanations begin to struggle. Perhaps there is a flourishing literature somewhere on such matters but in that case please direct me to it. The problem for environmental explanations is that they are good at showing why a group could be disadvantaged, but not why the distribution should be restricted, such that the process holds up the brightest BUT at the same time improves the dullest. This is not the first time this has been found. The white children in the 1960 normative sample of the Stanford Binet had a mean of 101.8 and a sd of 16.4, the black children from 5 southeastern states a mean of 80.7 and a sd of 12.4 (Jensen, Bias in mental testing, 1980, pg 99ff).  Jensen returned to this matter several times. A narrower distribution of ability has considerable implications for the numbers expected at the higher and lower levels of ability. There will be slightly fewer Africans at the lower end of the distribution (once the mean is taken into account) and, more visibly in public consciousness, fewer at the top range of ability, even once the lower mean has been taken into account.

Why are Africans so normal? Why are they so leptokurtic? Any suggestions welcome, including that their lack of Neanderthal genes makes them tend toward homogeneity.

The higher levels of math tilt for whites (compared to blacks) support differentiation theories (Deary et al., 1996 and Woodley, 2011). Differentiation theories predict that cognitive specialization in specific domains (math or verbal) increases at higher levels of ability. Because tilt reflects cognitive specialization, tilt levels were expected to be higher for whites, the higher ability group. This prediction was supported for math tilt (but not verbal tilt), which was higher for whites than blacks. The higher levels of math tilt for whites may reflect differential investment. Whites may invest more time and effort in math activities, perhaps by taking more math courses, which would yield higher levels of math tilt.

I must say that I doubt that anyone really invests more time and effort in maths unless they think there is a chance of being able to cope with the material. My personal calculation is that it would not be a good investment of my time because I would struggle too long, and can do better things by looking at simpler concepts, such as the representativeness of samples, the reliability and validity of measures, and the truthful depiction of simple statistics. All these ground-water problems run through much of psychology.

Coyle is on to this possibility: Whites generally showed math tilt in STEM and verbal tilt in the humanities, a pattern observed on all three tests (SAT, ACT, PSAT). In contrast, blacks showed this pattern for only one test (PSAT). The more consistent effects for whites can, again, be attributed to their stronger tilt bias, which presumably increased the likelihood of choosing a complementary major. This possibility is consistent with niche picking theories, which predict that people seek out and select activities that complement their interests and abilities (e.g., Scarr & McCartney, 1983). The pattern is also consistent with experience producing drive theory (Bouchard, 1997), which predicts that predispositions for certain activities shape behavior and experience. For example, predispositions for mathematics may lead to the acquisition of strong math skills in grade school, which in turn lead to the selection of STEM majors in college (e.g., engineering).

It should be emphasized that tilt was unrelated to g. Non-g factors generally have trivial predictive validity, but tilt is an exception ( Coyle, 2014). Tilt predicts specific abilities (this study; Coyle et al., 2014 and Coyle et al., 2015), educational achievements (Coyle et al., 2015, Lubinski et al., 2001 and Park et al., 2007), and occupational achievements ( Coyle et al., 2015 and Park et al., 2007). Moreover, tilt predicts achievements for both profoundly gifted subjects (top 1 in 10,000 in ability) ( Lubinski et al., 2001 and Park et al., 2007), and subjects in the normal range of ability ( Coyle et al., 2014 and Coyle et al., 2015). The current study is the first to demonstrate tilt differences for whites and blacks, two groups that differ substantially in g. 

This is a good paper, and is interesting both for what it includes and what it leaves out. It includes an important discussion about the way in which discrepancies are calculated, and you should read the paper for the full explanation. In essence, a discrepancy in abilities should also take into account how high those abilities are in absolute terms: at a high level of ability being good at both verbal and math might leave you without any apparent “tilt” but more demanding further testing would probably reveal it; at a low level of ability a discrepancy might leave you below a threshold for one type of problem solving, say for training or employment in some activity which requires maths. At a high level you would be able to do both easily and the discrepancy would be merely something which may influence choices within a very broad array of possible occupations.  

What the paper leaves out is a broader discussion of what the results mean. Sure, a racial difference in the pattern of abilities might have something to do with teaching and motivation. It is certainly worth investigating that further, as the paper suggests. However, it could also be that there is actually a difference in the pattern of abilities, such that Africans are inherently stronger on verbal than mathematical skills, even in the presence of good teaching in both. This is a testable hypothesis.

Although “tilt” is not related to g in these findings, there is a fundamental problem with school based exams, which is ensuring that verbal questions are as hard as maths questions. Different eras have demanded different things of school levers, and some harder maths exams might show even greater degrees of tilt. It is possible that language skills get to a ceiling sooner than maths skills, where complexity seems to have no limit. We certainly know from the Benbow and Lubinsky data on mathematically precocious youth that the brighter they were (even within the very high level of being 1 in 10,000) the more they gravitated to maths and science requiring occupations. Also, even within the billionaires those who were best at maths made more billions.

Postscript: In my early years I had Mr Henry, a good teacher in Maths, and then in my older years such bewildering lectures in higher mathematics from my Physics teacher (yes, I know higher maths is very different) that I gave it, up all too promptly. Perhaps everyone’s verbal/maths discrepancy has something to do with teaching, but it could be yet another case of teachers being blamed for the failings of their students.


  1. "Why are Africans so normal? Why are they so leptokurtic?"

    Have there been differences found between Eastern and Western African populations?

    My working, terribly Americentric theory: IIRC, most African Americans, for instance, are of Western African descent. There would be more variety in the gene pool for white Americans since they were ultimately descended from all over Europe. This would lead to a wider variety of abilities.

  2. Interesting, but why wouldn't any established population have the "full" range of abilities? Not saying to your theory, just asking the prior question.

  3. This comment has been removed by the author.

  4. Years ago I read a Liam Hudson book comparing "convergent" and "divergent" thinkers. He started by defining the two types in terms of "tilt" i.e. the difference in their scores on two different families of tests - something along the lines of "lateral"/"creative" versus logical/deductive.

    But he forgot; as the book progressed he talked as if "divergent" thinkers were defined by doing better on the tests of creativity (or whatever he called it) then did the convergent thinkers. But he was wrong: his original definition was perfectly compatible with convergent thinkers doing better than divergent thinkers on both sorts of tests, but with a different tilt.

    I mention this simply as an illustration that one probably has to be particularly careful not to fool oneself in a discussion of this type.

    Mind you, he was a bit of a twit was Hudson, and, I suspect, a bit of a spiv.

    1. Nice chap, caught the popular imagination, rushed everywhere with his thoughts, not a spiv, more of an innocent. Can remember having breakfast with him and Jensen before the famous 1970 Cambridge debate. Showed Jensen how to use a British public telephone.

    2. Sorry, should make it clear I taught Jensen about the use of letters and numbers on the telephone, while Hudson concentrated on getting him and all of us to the actual debate.

  5. Blacks are on average and especially the variety that was brought to the Americas, the less '' autistic-like '' or introvert. Introversion is related to high skills, the ability to focus on certain activities for a long time and / or have a strong inner psychological resistance against socialization. Most blacks are the exact opposite.

    Advanced mathematical skills are evolutionarily younger than verbal skills. However, I think wrong to suggest that the verbal skills have given what they had to give and mathematics has no ceiling. The human perceptual expansion in all its possibilities is limitless, at least for now.

    Real psychology in relation to the perceptual capacity (logical, rational and creative) is politically incorrect. Logical thinking / deductive and lateral / divergent need to be contextualized and used to the real world, to solve real problems, even in tests.

    Any test which measures potential within your understanding limit of what is measuring.

    Creativity is having awareness of one's own intuition. An internal capacity to perceive potentially useful ideas or value. Perceive yourself is the same to realize their own ideas. deeply internalize the information and usually pieces of it.

  6. White has a broader phenotypic variation in behavior of the East Asian and black. Of course, we will find a variation in all groups, but among whites the epicenter of dominant personalities seems to be less significant while the blacks, and especially the demographically large groups tend to be overwhelming extrovert while Asians generally tend to be overwhelming introverts.

    And personality tend to reflect in cognition to produce intelligence.

  7. Richard Lynn has data on this which I hope to post about later.

  8. My thoughts...

    It isn't "Africans" (or blacks) and "whites." It's a subset of each. How those subsets arose can influence the characteristics seen in a group.

    First, black students are much, much more likely than white students to attend schools that feature concentrated poverty:

    The SAT and ACT are achievement tests. Successive rewrites of the test have lessened its resemblance to an IQ test. It could be that lower scores on the test by black students reflect the lower expectations in the high schools with concentrated poverty at the time.

    Good math teachers are a rare and precious resource. The "tilt" may reflect a relative dearth of good math teachers in schools with concentrated poverty.

    1. It is possible that those factors affect the overall results. Don't see how it would affect the standard deviations. One could look to see what the effect of better maths teachers were on black and white students, and that analysis of variance could help test the hypothesis.

  9. James, you wrote:
    The white children in the 1960 normative sample of the Stanford Binet had a mean of 101.8 and a sd of 16.4, the black children from 5 southeastern states a mean of 80.7 and a sd of 12.4 (Jensen, Bias in mental testing, 1980, pg 99ff). Jensen returned to this matter several times …
    Why are Africans so normal? Why are they so leptokurtic? Any suggestions welcome …
    Well, this is a so-called good question. Are Africans really more normal? How normal are Hispanics?
    I found in CAT-ASSWAB97 data that young Whites (average of 12-17 year olds) disperse 14.56 on IQ g equivalents in representative data (mean 106.67) , Hispanics 14.06 (mean 97.07) , and Blacks 13.87 (mean 91.12). (Nyborg, 2015, Intelligence, 52, 44-62)
    So, we now see a racial hierarchy of “normality” with a South-North gradient. Evolution, in particular Cold Winter Theory (Lynn) may provide the answer.

    1. Helmuth, many thanks for your observations and additional data (which I should have recalled). Lynn says: An explanation for the smaller sd of blacks may be that whites gained new alleles for high IQ as mutations, posited in my Race Differences in Intelligence

    2. I believe E. Asians (including North East Asians) also tend to have a smaller SD than Whites. This would go against a cold weather/South-North gradient association. The general ancestries and places of origin of the Hispanics in question is also relevant.

    3. cont.: Hispanic groups of course vary widely in their degrees of European, African, and Amerindian ancestry (Amerindians being basically a cold adapted group).

    4. edit: " Hispanic groups of course can be very disparate in their (respective group average) proportions of European, African, and Amerindian ancestry....