By Bob
Williams
Most of psychometrics is based on statistical observation, for the obvious reason that there are multiple variables which usually cannot be held constant for research purposes. Mike has already explained the difference between correlation and variance. Perhaps the best way to visualize how the variance in one variable, X, relates to the variance in another one, Y, is to draw a square for each. The area of the X square (area = X2) represents its variance and the area of the Y square represents its variance. If X and Y are correlated, the two squares may be depicted as partially overlapping. Elements within the area of overlap are common to both variables.[1]
Some people look at a correlation of less than 0.5 and dismiss it by noting that the correlation must be squared in order to relate its variance to that of another variable.
Murray and Herrnstein: "A crucial point to keep in mind about correlation coefficients, now and throughout the rest of the book, is that correlations in the social sciences are seldom much higher than .5 (or lower than -.5) and often much weaker -- because social events are imprecisely measured and are usually affected by variables besides the ones that happened to be included in any particular body of data. A correlation of .2 can nevertheless be "big" for many social science topics. In terms of social phenomena, modest correlations can produce large aggregate effects. Witness the prosperity of casinos despite the statistically modest edge they hold over their customers."[2]
It is possible to measure IQ as well with chronometric tests as it is with traditional IQ tests. That is, the chronometric results correlate as well with IQ tests as IQ tests correlate with other IQ tests. This happens, even though individual response time (RT)[3] measures correlate from -.2 to -.4, sometimes less. But, when a battery of these tests are given, the end result is a correlation of up to 0.745.[4] The point is that even relatively small correlations produce variances which, in some situations, are additive. If you make enough measurements of additive components, the net measurement can be significant.
Another example of small, but meaningful and robust correlations is inbreeding depression. This phenomenon is observed to affect numerous traits, including IQ and is consistently mentioned in psychometric texts as one of the most indisputable proofs of the strong genetic component of intelligence. When inbreeding is very close (siblings or parent-child), the effect is quite large; but most studies are based on first cousins, where effects on physical traits are typically .05 sigma to .10 sigma.[5]
Arthur Jensen developed a means of statistical analysis which allows for a more penetrating view of correlations. He calls this the Method of Correlated Vectors and discusses it in Appendix B of The g Factor. Rushton has dubbed the method as “The Jensen Effect.”[6] There is no point in attempting to describe this rather complicated methodology here,[7] but it is worth mentioning, since it is a method which is more powerful than a simple correlation. The following example illustrates the difference between a simple correlation and a Jensen Effect:
“We can use the g loadings derived from the WISC standardisation sample of the same age group as was used in the pH study. For example, the correlated vectors between g and pH in a study of brain pH undertaken at Cambridge University gave a correlation of r = +.63, while the simple correlation between the WISC Full Scale IQ and pH was r = +.52 (Rae et al., 1996). The g loadings were derived from the standardisation sample, which is much larger and hence yields a more reliable g than the subject sample used in the measurement of pH levels. The correlated vectors analysis indicates that g, rather than other psychometric factors, is the chief source of covariance in the correlation between individual differences in IQ and in pH levels.”[8]
The variation in intelligence, especially as measured by psychometric g is known to be primarily the result of genetics. As recently as 20 years ago, this topic was still being debated, but now there exists a large body of replicated and diverse observations which demonstrate that g is not only highly heritable, but that it becomes more so as a function of age. Heritability is defined as the ratio of the variance in genotype to the variance in phenotype:
h2 =
genetic variance / phenotypic variance[9]
Where
the phenotypic variance is the sum of the genetic and environmental components.
The value of h2 is a function of the variance in the environmental component, since the environmental component is contained within the phenotype.
Even the most strident environmentalists (Flynn and Dickens, for example) contend that h2 is about 50%. The weight of evidence in the literature is that they are understating the number. So what is the correct number? Most sources put h2 at 0.70 for young adults, increasing to 0.80 for old adults.[10]
Chris Brand has claimed that broad heritability is about 75% with the remaining variance consisting of 10% due to environmental differences between homes, 5% due to other environmental influences, and 10% due to test unreliability.[11] Whatever the numbers, the real experts do not disagree much on the magnitudes; they do agree that social interactions are not a significant factor in the environmental variance. The environmental factors arise primarily through the intrauterine environment, breastfeeding, and the exposure to various chemical and biological agents. Jensen has observed that the balance of these factors is probably tilted in the direction of a net negative impact on intelligence.
In the foregoing discussion, the point was made that one area in which small correlations can be combined into a powerful measurement of g is in the area of elementary cognitive tests, which measure response times in different ways. Having made that connection, it is worth mentioning that as much as 70% of h2 is predicted by response time measurements. This is of such great importance that it has caused present day psychometric research to turn sharply in the direction of brain speed research. Brand, Jensen, and others have discussed this for years, but it is now front and center. Evidence of this can be seen from the papers presented this year at the International Society for Intelligence Research conference.
One of the important applications of the method of correlated vectors has been to demonstrate that g is virtually the only factor responsible for the correlations between RT and IQ tests.
It might be worth adding a few comments concerning the degree of sharpness separating purely genetic effects and purely environmental effects. This matter has been discussed from various perspectives in the literature. Starting on the genetic side, there is a concept developed by Lykken, which is called emergenesis.[12] He uses this term to describe observations of non-genetic behavior, which is most likely explained by genetic factors. Jensen has mentioned this concept in several publications. Lykken says that “the idea that an emergenic trait is an emergent property of a configuration of several or many independent or partly-independent genes. And one of the interesting facts about such emergenic traits is that, while certainly genetic, they will not tend to run in families.”
Without attempting to overly expound on the concept, the basic idea is that genetically determined traits may create a very strong predisposition for an individual to direct his life and behavior in particular directions. A simple example would be a person with particularly outstanding musical ability easily finding them and arranging his life to align with his natural abilities.
Throughout his book The g Factor: General Intelligence and Its Implications, Brand discusses the interaction of people with the environment and the interaction of the differences in genetic and environmental factors, which he designates as G x E. In spite of his lengthy discussion, Brand ultimately concludes that MZA studies reasonably demonstrate that the G x E result is almost entirely due to G.
The issue of G x E is not so easily dismissed as to prevent very strident commentators from suggesting that there are “huge” environmental effects on IQ. This argument has been advanced by William Dickens and James Flynn as an explanation of the Flynn effect.[13] It turns out that the arguments they present are hypothetical, unsupported by observations, and at odds with what is now known about the Flynn Effect (it is not g loaded).
[1] There is a long and through discussion of correlations and statistical analysis in Jensen’s Bias in Mental Testing. An illustration of the overlapping squares concept is depicted on page 193.
[2] The Bell Curve, page 67
[3] RT is defined as the time required by the brain to respond to an external stimulus.
[4] Jensen. The g Factor, p229
[5] Jensen reports a number of studies pertaining to inbreeding depression in his book The g Factor. See the chapter titled “The Heritability of g.”
[6] “Jensen's method of correlated vectors demonstrates that g (specifically a test's g loading) is the best predictor of that test's correlation with a given variable, in future, when a significant correlation occurs between g-factor loadings and variable X, the result might usefully be called a "Jensen Effect" (for that X variable). because otherwise there is no name for it, only a long explanation of how the effect was achieved. Naming it the "Jensen Effect" would honor one of the greatest psychologists of our time.”
The "Jensen Effect" and the "Spearman-Jensen Hypothesis" of Black-White IQ Differences by J. PHILIPPE RUSHTON, University of Western Ontario
[7] “Explaining how the method of correlated vectors works may possibly seem dauntingly complicated to all but the statistical-minded.” Jensen, The g Factor, p143 (I certainly will not argue with Jensen. This is not simple.)
[8] CORRELATED VECTORS, g, AND THE "JENSEN EFFECT" psycoloquy.99.10.082.intelligence-g-factor.19.jensen Fri Dec 31 1999 ISSN 1055-0143
PSYCOLOQUY is sponsored by the American Psychological Association
[9] See page 175, Jensen, The _g_ Factor; or, Miele, Intelligence, Race, and Genetics, P. 86
[10] Various references state much the same thing. Just a few examples:
Miele, F. (2002). Intelligence, Race, and Genetics: Conversations with Arthur R. Jensen
Sources
of human psychological differences: the Minnesota study of twins reared apart.
Thomas J. Bouchard Jr.; David T. Lykken; Matthew McGue; Nancy L. Segal; Auke
Tellegen Science, Oct 12, 1990 v250 n4978 p223(6)
L. S. Gottfredson, Intelligence 31 (2003) #4, p370 (referencing Robert Plomin)
[11] Brand, C. (1996). The g Factor: General Intelligence and Its Implications. Chichester, England: Wiley.
[12] DAVID T. LYKKEN (1982). Research With Twins: The Concept of Emergenesis
Psychophysology, The Society for Psychophysiological Research, Inc., Vol. 19, No. 4
A fascinating finding in this paper is that the score on the Raven’s test, divided by the average time spent thinking about each test item is an emergenic trait (very strong in MZ twins and essentially zero in DZ twins.
[13] William Dickens and James R. Flynn. Heritability Estimates vs. Large Environmental Effects: The IQ Paradox Resolved, Psychological Review, Vol. 108, No. 2 (April 2001)