## Race IQ and SES

Jensen (1998) makes a point that is worth repeating:

The pernicious notion that IQ discriminates mainly along racial lines, however, is utterly false.

Jensen presents what should be a predictable pattern for a highly heritable trait:

Source % of Variance Average IQ Difference
Between races (within social classes) 14 30 12
Between social classes (within races) 8 6
Interaction of race and social class 8
Between families (within race and social class) 26 65 9
Within families (siblings) 39 11
Measurement error 5 4
Total 100 17

This can be demonstrated most clearly in terms of a statistical method known as the analysis of variance. Table 11.1 shows this kind of analysis for IQ data obtained from equal-sized random samples of black and white children in California schools. Their parents’ social class (based on education and occupation) was rated on a ten-point scale. In the first column in Table 11.1 the total variance of the entire data set is of course 100 percent and the percentage of total variance attributable to each of the sources6 is then listed in the first column. We see that only 30 percent of the total variance is associated with differences between race and social class, whereas 65 percent of the true-score variance is completely unrelated to IQ differences between the races and social classes, and exists entirely within each racial and social class group. The single largest source of IQ variance in the whole population exists within families, that is, between full siblings reared together in the same family. The second largest source of variance exists between families of the same race and the same social class. The last column of Table 11.1 shows what happens when each of the variances in the first column is transformed into the average IQ difference among members of the given classification. For example, the average difference between blacks and whites of the same social class is 12 IQ points. The average difference between full siblings (reared together) is 11 IQ points. Measurement error (i.e., the average difference between the same person tested on two occasions) is 4 IQ points. (By comparison, the average difference between persons picked at random from the total population is 17 IQ points.) Persons of different social class but of the same race differ, on average, only 6 points, more or less, depending on how far apart they are on the scale of socioeconomic status (SES). What is termed the interaction of race and social class (8 percent of the variance) results from the unequal IQ differences between blacks and whites across the Spectrum of SES, as shown in Figure 11.2. This interaction is a general finding in other studies as well. Typically, IQ in the black population is not as differentiated by SES as in the white population, and the size of the mean W-B difference increases with the level of SES.

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1. I would point out that many of those numbers can vary substantially depending on the area under consideration. (How many races and social classes cohabit there, their group differences, etc.)

2. It seems paradoxical that the average difference between races (12 points) is larger than within families (11 points), yet the latter accounts for much more of the variance (39% against 14%). Does this just mean that there are more within-family differences to be counted? Or does it mean that although the *average* difference between siblings is slightly less than that between individuals of different races, the dispersion, and therefore the contribution to variance, is greater within families?

Could someone who understands analysis of variance better than I do comment on this?

3. Thrasymachus’s comment is correct.

David, the % variance numbers will depend on the precise composition of the populations whereas the average difference numbers merely reflect the magnitudes of the gaps.

For example, with the same BW gap, the % variance changes if you change the B/W ratio of the sampled population. Also, the relationship between the BW gap and the % variance explained by race is nonlinear. Adding a third racial group would also change % variance explained by race.

Family structure and SES structure add even more complication to that picture.

4. I haven’t really thought this through, and I have only a vague understanding of Analysis of Variance. But the quoted extract states that there were equal-sized samples of black and white children, so I don’t think the low proportion of between-race variance can be explained simply by lack of racial diversity in the sample: the study design guaranteed that between-race diversity would be given substantial weight. (Of course, I agree that if more races were added to the sample, the between-race contribution to total variance would probably be increased.)

I *think* the high proportion of within-family variance probably just reflects the fact that there are a lot of different families, and although the *average* difference between siblings is 11 points, there will be cases where the within-family difference is much larger, and therefore contributes a lot to the total variance. But please correct me if I’m in a muddle here.

5. David B: so I don’t think the low proportion of between-race variance can be explained simply by lack of racial diversity in the sample

no, to the contrary, that should overestimate the amount of variance between races.

the high proportion of within-family variance probably just reflects the fact that there are a lot of different families

note that there are two factors covered there: (1) Within families (siblings) and (2) Between families (within race and social class). Family size/composition should (off the top of my head) just shift variance between these two factors.

I don’t know ANOVA well enough to give a really satisfying answer to your question, but I played around with a simulated data set to see how things work out. It appears that there’s simply so much variance within groups (and within families) that the group partition (and a 1 SD gap) just doesn’t capture much of the the total variance.

6. Thanks. That sounds convincing.

Presumably where there is only one child in a family, it would be counted as a ‘family’ in itself, and would contribute to the between-families variance, but would not contribute to within-family variance (i.e. it would not be counted as a zero within-family deviation!)

7. …actually, it doesn’t matter if it *is* counted as a zero within-family deviation, since zero doesn’t add anything!

8. within-family variance is function of the genetic makeup of the family in question, and of the population in general. If you have a highly homogeneous inbred population, its variance will be lower than a hybrid heterogeneous one. You can see it in Brazil or South Africa, where in the same family you may have European looking blond children as well as African looking children. This happens less frequently in say Islandese or Hottentot families. I presume in families inbred for generations, living in small isolated islands, all the children are clone-likely similar, including in IQ.

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