One long standing problem with our traditional IQ tests is the ceiling effect: they measure accurately roughly up to the 99th percentile, but become exponentially inaccurate in measuring IQ’s past that ceiling. This is true despite what the IQ test may claim its ceiling to be. Indeed, you will hear that many tests (e.g., Raven’s) have ceilings beyond the 99th percentile.
So you might find that a crop of “high-range” IQ tests sprung on the internet. I suspect that they are doing a much better job at discriminating the top one percent, but one problem creators of these high-range tests face is accurately norming them.
So how do we accurately measure IQ’s in the top one percent, or at least accurately discover those individuals that have such IQ’s? Here’s a simple solution: have children at a sufficiently young age take an adult normed test and rank them against their peers. This is the basis of longitudinal studies on gifted children.
I found a longitudinal study on gifted individuals who, as twelve-year-old children, took the SAT’s (before the 1995 re-centering) and were categorized by their asymmetry of ability (e.g., verbal vs. mathematical aptitude). A 630 verbal score place a child in the 1 in 10,000 percentile for that ability; a 700 math score placed a child at the same percentile for that ability. There were some that achieved scores at those percentiles for both ability measures—they are the one’s who will become our intellectual giants.
Here are some interesting features of our precocious students. They were assigned to take a battery of cognitive tests one year later—as thirteen-year-olds—to further investigate their cognitive profiles:
. . .The Scholastic Aptitude Test (SAT), a test of developed verbal and mathematical reasoning ability of 17-year-olds (Donlon, 1984), is an especially good measure of reasoning among intellectually gifted 12- to 13-year-olds (Stanley & Benbow, 1986). From November 1980 through October 1983 the Study of Mathematically Precocious Youth (SMPY) conducted a national talent search for students who scored at least 700 on SAT-Mathematics before age 13 (Stanley, 1984a). During those three years, 292 such students were discovered. Almost concurrently, the Center for the Advancement of Academically Talented Youth (CTY) at Johns Hopkins conducted a national search for students who scored at least 630 on SAT-Verbal before age 13. CTY identified 165 students. It was estimated that such students represent the top 1 in 10,000 of their age group in the respective abilities. Several students (48) scored at least 630 on SAT-V and 700 on SAT-M before age 13.
As a service for the already identified mathematically precocious students, three supplemental cognitive testing sessions were held in May 1981, 1982, and 1983. Another testing session was held in May 1983 for the verbally precocious students identified in CTY’s 1983 Talent Search. Thus, only a small number of verbally talented students were tested. The data from these testing sessions were used in this study. A total of 144 students participated: 106 mathematically talented (termed 700M’s), 20 verbally talented (termed 630V’s), and 18 who met both the verbal and mathematics criteria (termed Doubles). At the time of testing subjects were approximately 13-years-old. . .
. . .Mean scores of the verbally and mathematically talented students, as well as of those both mathematically and verbally talented, for the various specific aptitude tests are shown by sex in Table 1. The mean scores of the examinees were, for the most part, equivalent to those earned by individuals at least five years older. On the spatial orientation test and especially on the spatial visualization test, these 13-year-olds scored above the average of college students. Even more impressive, however, were the scores on the nonverbal reasoning test. Relative to university students in England, this sample of extremely talented students scored at the 98th percentile on the Raven’s. The Bennett Mechanical Comprehension Test proved to be slightly more difficult. Even so, the mean score of these students was comparable to the average earned by 12th-grade males. We conclude that these students’ non-verbal aptitudes were highly developed. . .
As thirteen-year-olds, they already placed at the 98th percentile on the Raven’s matrices! But the fact that real differences in cognitive profiles emerged is even more interesting:
. . .Factor scores were then computed for each individual (Table 1) ANOV As by group (630V vs. 700M) and sex were then performed on the factor scores. The analyses showed that, for each factor, talent group was the significant variable ( p<.001 for the three factors). Sex and the group by sex interaction were not important. The performance of extremely mathematically talented students was superior to that of the extremely verbally talented students on the spatial/speed and nonverbal reasoning factors. For the verbal factor the verbally talented students exhibited higher performance.
Finally, an interesting trend was revealed. The presence of exceptionally high verbal ability appeared to increase the likelihood of the presence of high mathematical ability. Only one of the verbally precocious students had an SAT-M score lower than 500 (the average score of a college-bound 12th-grade male). The reverse was not apparent: high mathematical ability did not seem to indicate concomitantly high verbal ability. Twenty-two students scoring 700 or above on the SAT-M scored below 430 on the SAT-V (the average score of a college-bound 12th-grade male). These results, which were significantly different ( p < .05), indicate that verbally precocious students may be more evenly balanced in their cognitive profiles than mathematically precocious students. . .
We seem to have three real forms of ability: verbal, mathematical, and spatial. Those tilted mathematically performed better on the spatial tests than those tilted verbally. But all of them were far above average (of high school seniors) on all three abilities. I’m also fascinated by the asymmetry of verbal-math tilt. The presence of high verbal ability indicated high mathematical ability; but the converse isn’t true. I’m puzzling over how this feature now connects with my post on the brain anatomy of the mathematically gifted.
The irony is that Grady M. Towers knew about this divergence of ability (verbal vs. mathematical vs. spatial) from his own unpublished studies concerning high-IQ societies. He said:
8/24/98
Dear Kevin,
I know you never listen to me, but for once try to keep an open mind. I have something to teach you about factor analysis that took me a very long time to reason out, and which neither Dr. Jensen nor any other psychometrics researcher is likely to tell you. Perhaps they don’t actually know, though somehow I doubt it. Let me tell you why researchers can’t agree among one another about whether intelligence is one thing or many.
Let’s take a hypothetical test and give it to a hypothetical norming sample. This hypothetical test includes every kind of mental ability item ever found useful, each kind grouped into subtests with very low floors and very high ceilings. Each subtest has a very high internal consistency reliability (KR-20).
Now give this hypothetical test to 100,000 hypothetical subjects, take the correlations between the subtests, and factor analyze the results (principal factors–also called common factors). What would we find, hypothetically?
What we would find is one large general factor about twice as large in terms of variance as the sum of all the other sources of variance combined. We would find half a dozen to a dozen smaller factors (or bifactors), and an error factor accounting for about five percent of total variance.
Now take the same test, but instead of factor analyzing the full range of scores, factor analyze only the top 25 percent (roughly an IQ of 108 and above). Now you get different loadings. The large general factor goes down, but is still pretty large, while the special factors grow in size, and so does the error variance. But two or three of the special factors grow much more than the others.
Finally, do the same procedure on the top one percent. Now the general fac-tor and the two or three biggest special factors are the same size. There is no longer a general factor.
People who believe in a large general factor–such as Dr. Jensen–base their findings on a broad spectrum of ability drawn from the general population.
People who believe in Vernon’s hierarchical model of intelligence. Namely:
draw on range restricted data.
This model of intelligence was elicited from data supplied mostly by college students (roughly the top 25 percent of the IQ spectrum).
At still higher levels, g becomes small enough that we now have three coeval intelligences: fluid intelligence, crystallized intelligence, and spatial/mechanical ability. These are the same three major factors discovered by Horn and Cattell when they first named fluid and crystallized intelligence. They are also the three most important factors that turn up when I factor analyze Thurstone’s Primary Mental Abilities. (The description of factors given at the bottom of page 215 in Bias in Mental Testing is wrong.)
This has implications for the super-high IQ societies. Should the super-high IQ societies concentrate on only one of these as the true intelligence? Should there be a weighted or non-weighted average of two of them, or perhaps all three?
What we’ve done in the past is stress crystallized intelligence–Mensa to some extent, and ISPE very heavily. Triple Nine and Four Sigma tried to rectify that imbalance. The Mega Test was an attempt to weld two entirely different kinds of mental ability into a non-coherent whole.
Nobody has ever truly attempted to measure spatial/mechanical ability at super-high levels. Experiments have shown that some people can actually be taught how to visualize in four dimensions. I get glimmers of it myself when doing factor analytic studies. No super-high IQ society selects for this ability.
Frankly, I can’t see why this needs explanation. It should be perfectly obvious to anyone that Shakespeare could never have done what Newton did, nor could Newton have replaced Shakespeare. Nor could either of them have replaced Edison or van Gogh. The verbal form of intelligence took preeminence from the first days of intelligence testing because it predicts literacy and the literate run the world. Literate people are the organizers and manipulators–politicians, preachers, lawyers, CEOs, etc. Only in the last quarter of this century–because of computers–has the balance of power shifted in favor of pure puzzle solvers–the high level ability tapped by the LAIT or Mega non-verbal scales.
The only high-IQ society I ever truly enjoyed belonging to was Triple Nine. Most of them were or had been members of Mensa, so they were pretty high in verbal intelligence. Then the LAIT sifted out the very best puzzle solvers from this pre-selected verbally gifted group. They were fairly well read, but not overly burdened with educational credentials. They were broadly educated, but not deeply trained in some all-consuming specialty. They had no genius, but common sense was as ubiquitous as dirt. I liked them a lot, and miss them still. It’s too bad that the invasion from ISPE was allowed to destroy the best of the best.
For more on the precocious students, see David Lubinski’s site here. He actually discusses the importance of testing for spatial ability to further discriminate for super precocious children. Here is the abstract of his paper:
Students identified by talent search programs were studied to determine whether spatial ability could
uncover math-science promise. In Phase 1, interests and values of intellectually talented adolescents
(617 boys, 443 girls) were compared with those of top math-science graduate students (368 men,
346 women) as a function of their standing on spatial visualization to assess their potential fit with
math-science careers. In Phase 2, 5-year longitudinal analyses revealed that spatial ability coalesces
with a constellation of personal preferences indicative of fit for pursuing scientific careers and adds
incremental validity beyond preferences in predicting math-science criteria. In Phase 3, data from
participants with Scholastic Aptitude Test (SAT) scores were analyzed longitudinally, and a salient
math-science constellation again emerged (with which spatial ability and SAT-Math were consis-
tently positively correlated and SAT-Verbal was negatively correlated). Results across the 3 phases
triangulate to suggest that adding spatial ability to talent search identification procedures (currently
restricted to mathematical and verbal ability) could uncover a neglected pool of math-science talent
and holds promise for refining our understanding of intellectually talented youth.
More on this in the future.
Posted on 18 February 2009
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