Arthur R. Jensen (1999) Correlated Vectors, g, and the "jensen Effect". Psycoloquy: 10(082) Intelligence g Factor (19)

Reply to Rushton on Jensen on Intelligence-g-Factor

Educational Psychology

School of Education

University of California

Berkeley, CA 94720-1670

nesnejanda@aol.com

The "method of correlated vectors," which Rushton (1999) has dubbed the "Jensen Effect," was devised as one method for discovering non-psychometric correlates of psychometric g. It plays an important role in my book and could probably be applied even more extensively to data analyses already reported in the psychological literature.

1. Rushton (1999) is right: My main interest is in the understanding of g as a scientific construct. From a purely scientific standpoint, understanding the nature of g seems primary, not only because it is the basis of the practical validity of the psychometric tests of mental ability used in schools, in employment, and in selection for college and for training programs in industry and the Armed Forces, but because it also plays a central role in our attempts to understand the various educational, social, and economic problems that exist in every increasingly technological and information-intensive society.

2. The g factor is usually the largest single source of variance in a battery of diverse psychometric tests, and although it is only one of many linearly independent factors that can be extracted from these tests, it has larger correlations with a wider variety of psychometric variables than any other factor. The method of correlated vectors is an efficient and precise method for screening the g factor's (or other factors') relevance to other, non-psychometric variables. What Rushton has named the "Jensen Effect" (to obviate having to repeatedly describe in detail the methodology for the resulting phenomenon) occurs when the column vector consisting of the g loadings of the n subtests in a battery is highly and significantly correlated with the corresponding column vector of those n subtests' correlations with some directly measurable non-psychometric variable. As Rushton points out, the "Jensen Effect" has been found for a considerable number of such variables, including those related to the heritability of the tests, the effects of inbreeding depression, and various physiological brain correlates of diverse tests. Although correlations are, of course, not necessarily causal, they do afford the best clues we can obtain of where to look for the causal mechanisms using other methods of investigation. The "Jensen Effect" is not at all inevitable and does not materialize for certain variables, for example, the variable known as "inspection time" (IT), or the exposure time required by a person to make a simple sensory discrimination, such as detecting the difference between two parallel straight lines that differ in length by a ratio of 2 to 1. Although IT performance is correlated with IQ and with the g factor, it has a stronger association with a lower-order perceptual speed factor (Deary & Crawford, 1998).

3. Here Rushton's exposition of the "Jensen Effect" may risk confusing readers by not emphasising the clear distinction between the simple or direct correlation between two variables and the "Jensen Effect," which is the correlation between two vectors each compsed of n elements. If one wanted the simple correlation between g and, say, brain size, to use Rushton's example, one would simply correlate a number of individuals' g factor scores with their brain-size measurements. But g factor scores are not factor pure; they also have some small proportion of variance from all of the lower-order factors in the test battery. The method of correlated vectors allows one to see which unadulterated factors in the test battery are the most clearly related to the external variable of interest. The g factor scores (but not the g factor loadings) are the most vulnerable to some degree of contamination by other, non-g factors in the matrix; other non-g factor scores derived by regression methods are purer measures of their factors than are g factor scores (which are just a g-weighted average of the individual's standardized scores on the various tests'). But actually the most valuable advantage of the method of correlated vectors is its meta- analytic property -- it can be applied to data obtained from different published studies and different subject samples. For example, Study A shows the correlations of, say, brain intracellular pH with each of the 12 subtests of the Wechsler Intelligence Scale for Children (WISC), but does not give the g loadings of the subtests or the correlation matrix that would permit the extraction of the g factor. 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.

4. The standardised magnitudes of the White-Black differences on a wide variety of tests consistently shows a strong "Jensen Effect" in over twenty independent studies. Other factors independent of g contribute comparatively little to the difference, only a spatial reasoning factor showing a consistent but relatively small effect. The subtests of IQ batteries are not at all homogeneous in their contributions to the overall W-B difference in IQ; nearly all of the difference is contributed by g, the one factor common to all cognitive tests. This seems to me an important discovery, not because it proves anything about causation, which correlation alone cannot do in any case, but because it narrows and focuses the phenomenon in need of explanation. Rushton seems to appreciate this value of my investigation as some other reviewers of "The g Factor" apparently have not.

5. One new application of correlated vectors that was not included in "The g Factor" (Jensen, 1998, 1999) is in the study of children's mental growth trends on a large battery of diverse tests, a research project now in preparation for publication. The vector of the tests' g loadings is highly correlated with the vector of standardised test score differences between age groups of school children that differ by one to two years. It appears that mental growth is manifested most strongly in those tests with the largest g loading. Moreover, it is found that the pattern of age-group differences (of 2-years) within either the White or the Black samples is statistically indistinguishable from the pattern of W-B test-score differences in W and B groups of the same age. The mental growth trajectories of W and B children on a set of diverse tests have essentially the same pattern of g loadings and the age-to-age mean subtest scores differ only in their slopes and asymptotes. To explain this finding solely in terms of test bias and cultural differences would mean that these racial-cultural influences perfectly simulate chronological age differences in test scores within each racial group.

Deary, I. J., & Crawford, J. R. (1998). A triarchic theory of Jensenism: Persistent conservative reductionism. Intelligence, 26, 273-282.

Rae, C., Scott, R. B., Thompson, C. H., Kemp, G. J., Dumughn, I., Styles, P., Tracy, I, & Radda, G. K. (1996). Is pH a biochemical marker of IQ? Proceedings of the Royal Society (London), 263, 1061-1064.

Jensen, A. (1998). The g Factor: The Science of Mental Ability. Praeger

Jensen, A. (1999). Precis of: "The g Factor: The Science of Mental Ability" PSYCOLOQUY 10(23). ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1999.volume.10/ psyc.99.10.023.intelligence-g-factor.1.jensen http://www.cogsci.soton.ac.uk/cgi/psyc/newpsy?10.023

Rushton, J.P. (1999). The "Jensen Effect" and G Vector Analysis. PSYCOLOQUY 10(44) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1999.volume.10/ psyc.99.10.044.intelligence-g-factor.3.rushton http://www.cogsci.soton.ac.uk/cgi/psyc/newpsy?10.044