hypothesized genetic racial differences in iq: a criticism of three proposed lines of evidence

Behavior Genetics, Vol. 10, No. 2, 1980

LETTER TO THE EDITOR

Hypothesized Genetic Racial Differences in IQ: A Criticism of Three Proposed Lines of Evidence

Brian M a c k e n z i e 1

Received23 Oct. 1979

Three lines o f reasoning are discussed which have been put forward by A. R. Jensen in support o f the hypothesis o f genetic racial differences in IQ. These are the probabilistic connection o f heritability to between-group genetic differences, the theoretical or formal relationship o f within-group heritability to between-group heritability, and the regression o f the IQ scores o f blacks and whites to different population means. The first is shown to be a purely empirical claim that has no value as evidence in the absence o f substantial confirming data, which are not available. The second and third are shown to be purely formal implications o f the statistical models used to describe between-group heritability and linear regression, with no implications for the validity o f the hypothesis. The attempted use of all three to support the hypothesis o f genetic racial differences in IQ is discussed as an example o f the fallacious reification of abstract methodology.

KEY WORDS: A. R. Jensen; intelligence; race differences; heritability; IQ.

INTRODUCTION

First I shall state what this article is not. It is not an attempt to prove or disprove--or marshall evidence for or against--the hypothesis of genetic racial differences in IQ. It is instead a critical examination of some of the evidence and reasoning which have been put forward in support of the hypothesis. It therefore addresses Art rather than Nature, the literature on the hypothesis rather than the hypothesis itself. If it has a moral, it is a methodological moral, concerning how our methods of investigation can

1 Department of Psychology, University of Tasmania, GPO Box 252C, Hobart, Tasmania 7001, Australia.

225

0001-8244/80/0300-0225503.00/0 �9 1980 Plenum Publishing Corporation

226 Mackenzie

mislead us, rather than a substantive moral, about the existence or nonexistence of genetic racial differences. Such methodological morals can be critically important ones, however, since our methods and the literature that embodies them provide our only means of trying to answer the substantive question.

A. R. Jensen has written many articles and books dealing in large part with genetic factors in IQ, including genetic factors in the observed black-white differences in IQ in U.S. populations (e.g., Jensen, 1969, 1972, 1973a,b, 1978). In these, he reviews the evidence for the existence of an approximately 15-point mean difference in IQ between blacks and whites, and then contrasts environmental and genetic explanations for the difference. While never suggesting that the difference is entirely due to genetic racial factors, he concludes that a substantial proportion of it probably is. He bases this conclusion on many lines of evidence, and it is not always clear which of them are intended to have the greatest weight. Here, I will review three of them. They may or may not be the ones which Jensen considers most important, but they are all ones which he emphasizes at several points in his writings. At the same time, they are ones which are relatively easy to extract from his overall analysis without distortion due to their being taken out of context. These three lines of evidence are, in brief, the probabilistic connection between a character's heritability within groups and its heritability (or the magnitude of the genetic contribution to the difference) between groups, the formal theoretical connection between the two kinds of heritability, and the regression of IQ scores of blacks and whites to different population means.

To assess these specific lines of evidence, I must treat some background issues as settled, even if they could be disputed in their own right. Accord- ingly, for the purpose of this review, I will assume that the 15-point mean black-white IQ difference has been accurately and reliably measured, that heritability analyses can properly be applied to IQ data, that the heritability of IQ in the U.S. white population is around 0.80, and that in the black population (for which fewer data are available) the heritability is com- parably high. These assumptions are, of course, all consistent with Jensen's position.

PROBABILISTIC CONNECTIONS

Given that the heritability of IQ is substantial in both the white and the black populations, what can be said about the source of the difference between the two populations? The two sources of differences (within and between groups) are of course logically separate. There is, however, Jensen maintains, a probable or likely relationship between the two. In his 1969 paper he wrote:

Genetic Racial Differences in IQ: A Criticism 227

While it is true that heritability within groups cannot prove heritability between group means, high within group heritability does increase the a priori likelihood that the between groups heritability is greater than zero. In nature, characteristics that vary genetically among individuals within a population also generally vary genetically between different breeding populations of the same species. (Jensen, 1972, p. 162)

Jensen's claim was criticized by Lewontin (1970), who cited plant breeding examples to show that the within- and between-groups genetic factors could vary independently. In one pair of plant samples in Lewontin's example, the heritability of a character (height) was 1.0 within each, while the mean difference between the two was entirely environmental. In another pair of samples, the heritability of the same character was 0.0 within each, while the mean difference between the two samples was entirely genetic in origin.

In reply, Jensen (1970) insisted quite rightly that a single extreme case provides no evidence against a general trend, and clarified his position as follows:

The real question is not whether a heritability estimate, by its mathematical logic, can prove the existence of a genetic difference between two groups, but whether there is any probabilistic connection between the magnitude of the heritability and the magnitude of group differences. Given two populations (A and B) whose means on a particular characteristic differ by x amount, and given the heritability (hA 2 and hB 2) of the characteristic in each of the two populations, the probability that the two populations differ from one another genotypically as well as phenotypically is some monotonically increasing function of the magnitudes of hA s and h~ 2. (Jensen, 1970, pp. 21-22)

In his reply, however, Jensen does not quite address the significance of the example. Since the within-group and the between-group factors can vary independently, the connection between them, whether logical or probabilistic, cannot be intrinsic or inherent. It can only be an empirical relationship, depending on the observed relationship of within-group and between-group genetic factors in an adequately large sample of other characters. If we had sufficient data on the heritability and the between- group genetic influences on a variety of characters, and if the data indicated that such a relationship was present, we could indeed say, since the heritability of this character is x in each group, the probability of there being no between-group genetic difference is no more than p. If we could quantify the between-group genetic differences in the sample, we could say even more. We could correlate the within- and the between-group heritabilities in our sample of characters and, for any other character of interest, predict its between-group heritability by simple regression from its within-group heritability. In either case, however, the relationship would be a purely empirical one, independent of genetic theory. Both the existence and "the size of the relationship could be estimated only from a substantial body of data.

However, Jensen does not support his claim with the necessary data on within- and between-group genetic factors in other characters. Sufficient

228 Mackenzie

data for the purpose do not exist. Instead, he repeatedly (e.g., 1970, p. 22; 1973a, p. 135) emphasizes a single example, that of the mean difference in height between pygmies and Watusis. He argues at length that it is highly plausible that the mean difference between the two has a genetic component. But whether that single character is influenced by a genetic between-groups factors or not is irrelevant. To generalize to another specific character it is necessary to have information on the within- and between- group genetic factors in a variety of characters. A single example provides no evidence for or against a general trend, whether it is Lewontin's com- pletely certain example or Jensen's merely plausible one. Even if the within- and between-group genetic factors controlling height in Jensen's example were known precisely, the single example would constitute no evidence for the generalizing of their relationship to any other character.

The assessment of Jensen's claim about the relationship of within- group to between-group genetic influences through probabilistic connections is therefore simple. It is a purely empirical claim that is empty without hard data to back it up; and there are no hard data. It may seem curious that the claim about probabilistic connections should ever be thought to have value as evidence (or even as argument) at all. A specific contentious hypothesis about between-group genetic differences is supported only by restating the hypothesis in general terms.

FORMAL THEORETICAL CONNECTIONS

The second line of evidence depends on a simple use of rather more technical statistical procedures that have been incorporated into genetic theory. It is the theoretical connection of within-group to between-group heritability. Jensen emphasizes this relationship in all the major papers cited (1969, 1973a,b, 1978). In one he writes:

Theoretically it is quite erroneous to say there is no relationship whatsoever between heritability within groups and heritability between group means. Jay Lush, a pioneer in quantitative genetics, has shown the formal relationship between these two heritabilities (Lush, 1968, p. 312), and it has been recently introduced into the dis- cussion of racial differences by another geneticist, John C. DeFries [1972]. This formulation of the relationship between heritability between group means (hB 2) and heritability within groups (hw 2) is as follows:

(1 - r )p h~ 2 ~ hw ~

(1 - , ) r

where h~ 2 is the heritability between group means; hw 2 is the average heritability within groups; r is the intraclass correlation among phenotypes within groups (or the square of the


point biserial correlation between the quantized racial dichotomy and the trait measurement);

p is the intraclass correlation among genotypes within groups, i.e., the within-group genetic correlation for the trait in question.

Since we do not know 0, the formula is not presently of practical use in determin- ing the heritability of mean group differences. But it does show that if for a given trait the genetic correlation among persons within groups is greater than zero, the between-group heritability is a monotonically increasing function of within-groups heritability. (Jensen, 1973a, p. 146)

He then presents a graph (which appears also in Jensen, 1973b, p. 410) showing how the between-group heritability varies as a joint function of the genetic intraclass correlation and the within-group heritability for the character in question.

Jensen is perfectly correct; the between-group heritability does increase as a function of both the within-group heritability and the genetic intraclass correlation, and as long as both these quantities are greater than zero the between-group heritability will also be greater than zero. Unfortunately, as Jensen points out, the genetic intraclass correlation is not known in the case of IQ. But does this clear relationship at least increase the plausibility, or the likelihood, of the existence of between-group genetic differences in IQ, even if they cannot be precisely quantified?

The answer is no, it does not. The genetic intraelass correlation does not help to provide evidence for between-group genetic differences; it is a measure of them. Any intraclass correlation involves a comparison of the variance within groups to the variance between groups. 2 The between-group variance is one of the terms in the equation. However, whether there is any between-group genetic variance in IQ is precisely the point at issue. Our inability to calculate the genetic intraclass correlation is not simply a practical limitation on our knowledge, preventing us from using it to demonstrate the existence of between group genetic differences. We could not, even in a state of perfect knowledge, calculate the genetic intraclass correlation and use it as evidence for the existence of such differences, simply because in order to make the calculation we would have to measure the differences first. I f we could calculate the genetic intraclass correlation, we would never argue about the question of between-group genetic differences, because we would already have measured them. Yes, there are between-group genetic differences, of such and such a magnitude, and they are part of the reason why the genetic intraclass correlation is this particular size; or no, there are no between-group genetic differences, and for that reason the genetic intraclass correlation is zero. In either case, the measure-

2 This fact may be obscured for statistically unsophisticated readers by Jensen's definition of the genetic intraclass correlation simply as "the within-group genetic correlation" and "the genetic correlation among persons within groups," rather than as a form of comparison of within-group and between-group factors.

230 Mackenzie

ment of the between-group genetic differences is both logically and opera- tionally prior to the determinat ion of the genetic intraclass correlation, a

This clarification of the relationship between the genetic intraclass correlation and between-group genetic differences allows us to assess Jensen's reasoning on the matter. Jensen discusses the relationship o f within-group to between-group heri tabi! ~y as part of his argument for the plausibility, at least, of the existence of between-group (racial) genetic differences. He is careful not to state explicitly that this relationship d e m o n s t r a t e s the existence o f such differences, but it is presented as one of a series of argu- ments to show their likelihood. However, in basing this a rgument for the likelihood of between-group genetic differences on a concept (between- group heritability) which depends on the genetic intraclass correlation, which in turn depends on measurement of precisely those genetic group differences for the existence of which he is arguing, Jensen presents an argument which is circular and otiose. Again, it may seem curious that these "theoret ical connect ions" should ever be put forward as part of an argument for the existence of genetic racial differences in IQ at all. A specific contentious hypothesis about between-group genetic differences is supported by describing some of the nonmeasurable statistical relationships into which any such genetic differences would enter.

R E G R E S S I O N TO D I F F E R E N T P O P U L A T I O N M E A N S

The third line of evidence is also statistical but is based on precisely measurable relationships. No t only do the black and white populations in the United States have mean IQs that are separated by about 15 points, but likewise the predicted scores of individual black and white subjects regress to these different populat ion means. Jensen (1973a) draws the presumed implications of this fact very clearly:

The correlation among siblings of close to 0.40 on the Lorge-Thorndike Intelligence Tests in both the white and the Negro samples has an interesting consequence which

A similar point is made briefly by Feldman and Lewontin (1975), where they conclude "The suggestion that h~ z is in some way predictable from hw 2, or that the size of hw 2 in some way contains information about the size of hn 2, is entirely spurious." Plomin and DeFries (1976) take exception to their conclusion, writing: "Surely they cannot mean that all noncausal mathematical relations are spurious." Presumably, Feldman and Lewontin did not mean any such thing; their objection was properly to the attempt to use a nonempirical mathematical formalism (DeFries's equation) as evidence for the occurrence with a greater than zero value of a variable (between-groups genetic differences) corresponding to one of the terms implicit in the formalism (between-groups genetic variance). Unfortunately, Feldman and Lewontin (1976), in replying to Plomin and DeFries, did not clarify their position on the network of logical and empirical issues involved. Instead, they contented themselves with making sar- castic statements about mathematical relations between randomly chosen variables. The essential validity of their previous conclusion may therefore have been obscured for readers who were following the controversy.


may seem puzzling from the standpoint of a strictly environmental theory. It is entirely expected if one assumes a genetic model of intragroup and intergroup differences. This is the phenomenon of sibling regression toward the population mean . . . . Genetic theory predicts the precise amount of regression.

[I]f we match a number of Negro and white children for IQ and then look at the IQs of their full siblings with whom they were reared, we f i n d . . . [that] the Negro siblings average some seven to ten points lower than the white siblings. Also, the higher we go on the IQ scale for selecting Negro and white children to be matched, the greater is the absolute amount of regression shown by the IQs of the siblings. For example, if we match Negro and white children with IQs of 120, the Negro siblings will average close to 100, the white siblings close to 110. The siblings of both groups have regressed approximately halfway to their respective population means and not to the mean of the combined populations. The same thing is found, of course, if we match children from the lower end of the IQ scale. Negro and white children matched for, say, IQ 70 will have siblings whose average IQs are about 78 for the Negroes and 85 for the whites. In each case the amount of regression is consistent with the genetic prediction. The regression line, we find, shows no significant departure from linearity throughout the range from IQ 50 to 150. This very regular phenomenon seems dif- ficult, to reconcile with any strictly environmental theory of the causation of individual differences in IQ that has yet been proposed. If Negro and white children are matched for IQs of, say, 120, it must be presumed that both sets of children had environments that were good enough to stimulate or permit IQs this high to develop. Since there is no reason to believe that the environments of these children's siblings differ on the average markedly from their own, why should one group of siblings come out much lower in IQ than the other? (Jensen, I973a, pp. 117-118)

At first look, the reasoning may seem to have an air of elegance about it. If the black and the white children are matched for IQ, and if children have roughly the same environment as their siblings, and if the black siblings' IQs tend toward a lower mean than the white siblings' IQs, then what can be responsible for the black-white difference if not some innate racial difference, some genetic difference between the groups? The black children with IQs of 120 are much more extreme cases, much more removed from their population mean, than are white children with IQs of 120; and more extreme values lead to greater amounts of regression. The population mean, encoded perhaps in the gene pool of the race, exerts a pervasive influence, even though we start with individuals with the same phenotypic or observed value of the character.

In fact, the reasoning is not elegant at all. It is quite fallacious, and is based on a simple confounding of genetics and statistics. Jensen states that the precise amount of regression is predicted by genetic theory. It is not. Genetic theory never comes into the matter at all, except insofar as it incor- porates elementary statistical models. The precise amount of regression is predicted, by linear regression, only from the sibling correlation and the population mean and variance. Given a sibling correlation of 0.4, it follows necessarily that the regressed or predicted score will be "precisely" 4/10 as far from the population mean as the predictor score is, whatever the population mean may be. The population mean and the sibling correlation together unequivocally determine the degree of regression; it is inconceivable that any scores could regress "to the mean of the combined populations." The

232 Mackenzie

fact that the black siblings regressed to a lower population mean than the white siblings is not explained by any environmental or any genetic factors; it is explained only by the fact that the black population mean is lower.

To clarify the point, consider an example in which no genetic mechanisms will be suspected. Let us assume that the market value of houses within neighborhoods is correlated 0.50 with the market value of the house next door. We will look at two neighborhoods. In Seaview Estate, the mean value of houses is $60,000. In Sandy Flats, it is $50,000. For sim- plicity, we will assume that the standard deviation is $10,000 in both, and that house values are normally distributed within each neighborhood. We now select houses in both neighborhoods with market values of, say, $70,000. Having matched house values between groups, we ask, what is the predicted value of the house next door to the $70,000 house in each neighborhood? We will not be surprised t o find that the houses next door to $70,000 houses in Sandy Flats have a lower predicted value--and a lower mean value--than the houses next door to $70,000 houses in Seaview Estate. In Sandy Flats, the mean next door value will be $60,000, halfway back to the population (neighborhood) mean of $50,000. In Seaview Estate, the mean next door value will be $65,000, halfway back to the population mean of $60,000. We will not be surprised, precisely because Sandy Flats has a lower mean value; naturally, therefore, the predicted values for individual houses will be lower also.

And so it is with the IQ scores of black and white siblings. The population mean, and hence the whole distribution of scores, is lower for blacks than for whites. Naturally, therefore, the predicted values for individual blacks will also be lower than for individual whites. There is no need, and no possibility, of invoking a separate explanation, genetic, environmental, or otherwise, for the greater regression of the black siblings' scores. It is simply a statistical consequence of the lower mean.

Once again, it may seem curious that the greater regression of the IQ scores of blacks should ever be put forward as evidence for the existence of genetic racial differences in IQ. Jensen uses a necessary consequence of the lower mean IQ of blacks, that blacks' IQ scores will regress to this lower mean, as evidence for a specific contentious hypothesis to explain this lower mean score, that it is due to genetic racial differences. He takes the phenomenon to be explained, describes its statistical properties, and uses these properties as evidence for an explanation of the phenomenon.

CONCLUSION

There is a disturbing similarity in the three examples cited. In each, the hypothesis of genetic racial differences is stated in terms of the technical


vocabulary which is used in a relevant scientific specialty, but which vocabulary has of course no implications for the correctness or incorrectness of the hypothesis: But for Jensen, use of the technical language itself, of probability, population genetics, and statistical regression, is apparently taken to provide evidence in favor of the hypothesis. The implicit assump- tion seems to be that if the hypothesis and its implications can be expressed in the language of a technical specialty, then the authority of that specialty can be invoked in support of the hypothesis. If this reconstruction is valid, then Jensen's reasoning is merely an extreme and transparent example of the scientism and methodolatry that has sometimes characterized our field: if it looks scientific, it must be scientific, and if we can clothe our ideas in the trappings of scientific method, then those ideas must have the weight of scientific method behind them. Jensen's case is extreme, but is not otherwise unique. We are frequently too ready to attribute explanatory power to purely formal manipulations, transforming our data so that they look different and then claiming that the transformation amounts to evidence for an explanation. We substitute statistical analysis for a thorough attempt at causal and theoretical analysis, because the statistical analysis conveys a greater, if misguided, sense of precision (cf. Lewontin, 1974). We thereby reify our methods, sometimes our abstract or statistical ones as in the examples here, sometimes our experimental ones, and believe that adherence to them is itself sufficient to lead us to theoretical understanding. But as these small case histories try to illustrate, and as I have tried to show elsewhere in a broader context (Mackenzie, 1977), an uncritical reliance on formalized methodology alone leads only to error and confusion.

REFERENCES

DeFries, J. C. (1972). Quantitative aspects of genetics and environment in the determination of �9 behavior. In Ehram, L., Omenn, G. S., and Caspari, E. (eds.), Genetics, Environment, and

Behavior, Academic Press, New York. Feldman, M.W. , and Lewontin, R. C. (1975). The heritability hangup. Science

190:1163-1168. Feldman, M. W., and Lewontin, R. C. (1976). Letter to the editor. Science 194:12-14. Jensen, A. R. 0969). How much can we boost IQ and scholastic achievement? Harvard Educ.

Rev. 39:1-123. Jensen, A. R. (1970). Race and the genetics of intelligence: A reply to Lewontin. Bull. Atom.

Sci. 26(5): 17-23. Jensen, A. R. (1972). Genetics and Education, Methuen, London, Jensen, A. R. (1973a). Educability and Group Differences, Methuen, London. Jensen, A. R. (1973b). Educational Differences, Methuen, London. Jensen, A. R. (1978). The current status of the IQ controversy. Aust. PsychoL 13:7-28. Lewontin, R. C. (1970). Race and intelligence. Bull. A tom. Sci. 26(3):2-8. Lewontin, R. C. (1974). The analysis of variance and the analysis of cause. Am. J. Hum. Gen.

26:400-411.

234 Mackenzie

Lush, J. L. (1968). Genetic unknowns and animal breeding a century after Mendel. Tr. Kansas Acad. Sei. 71:309-314 (cited in Jensen, 1973a).

Mackenzie, B. D. (1977). Behaviourism and the Limits of Scientific Method, Humanities Press, New York.

Plomin, R., and DeFries, J. C. (1976). Letter to editor. Science 194:1 t-12.

hypothesized genetic racial differences in iq: a criticism of three proposed lines of evidence

Documents