Educability-and-Group-Differences-1973-by-Arthur-Robert-Jensen

216 Educability and Group Differences
of a and A alleles are equal, i.e., the proportions are 0-5a+0-5A.
Since every individual receives two alleles (one from each parent),
the proportions of all possible combinations10 of the alleles in the
population (assuming random mating - a simplifying but not a
necessary assumption) is given by the binomial expansion of
(•5a + -5A)2, which is
0-25aa + 0-50aA 4- 0-25 AA.
The frequency distribution, with three categories (or ‘scores’), will
thus have one-fourth of the population in the low category, onehalf
in the ‘average’ or intermediate category, and one-fourth in
the high category. Now consider a hypothetical population Y, in
which the proportions of a and A alleles are 0-6 and 0-4, respectively.
In this case, the expansion of (0*6a + 04A )2 is
0-36aa + 0*48aA + (H6AA
and 36 percent are in the low category, 48 percent in the intermediate
category, and 16 percent in the high category.
If we assign the value of 1 to A and 0 to a, the mean of population
X will be 1-00 and the mean of Y will be 0-80. The variance is
0-50 in population X and 0*48 in population Y. Also, the distribution
in population X is symmetrical, while the distribution of
Y is skewed to the right. If, in producing the next generation of
population X, we assume perfect assortative mating and no loss
of genes through selection, the mean would remain 1-00, but the
variance would increase to 0-75. (The proportions would be
0-375aa + 0-250aA + 0-375AA.) We can see that assortative mating
increases variance in the population by increasing the proportions
of homozygotes (individuals with the same alleles on both chromosomes,
i.e., AA and aa) and decreasing the proportion of
heterozygotes (i.e., Aa).11
NOTES
1. Note that ‘accounted for’ does not mean ‘caused by’. Correlations
(zero, order, multiple, or partial) do not and cannot demonstrate
causality, although they are a useful basis for hypothesizing causal
factors which then must be proved to be causal by other than
correlational methods.