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

Race Differences in Intelligence 199
possible subpopulation differences in assortative mating, test
reliability, and ‘range-of-talent’ (i.e., differences in variance).
14. We shall assume only true-score variance in this model. In practice,
variance due to measurement error (test unreliability) can be
determined and removed at any one of several stages in the
analysis. It is simplest to remove it from the total variance at the
outset.
15. In this example we assume random mating for the sake of simplicity.
In practice, we take assortative mating into account. Under random
mating, one-half of the additive genetic variance is within families
for DZ twins (and ordinary siblings) and one-half is between
families. The effect of assortative mating (correlation between
parents) is to proportionally decrease variance within families and
increase variance between families. When the correlation between
parents is 0-50, the proportions of between- and w*7/tm-families
genetic variance are about 0-60 and 0-40, respectively.
16. The variance ratio, labeled F after Sir Ronald Fisher, the English
geneticist and statistician who invented the method known as ‘the
analysis of variance’, is explicated in virtually all modern statistical
textbooks, e.g. Walker and Lev (1953).
17. It is possible, however, to obtain Holzinger’s (1929) H coefficient
- a kind of index of heritability - from the F ratio. H — (F —1 )/F.
H has been frequently called heritability, but it is actually not the
same as h2, which is VGIVP, i.e., the proportion of genetic variance.
H — {VWDZ—VWMZ)IVWDZ. [Or, from twin correlations, H =
(rMZ —rDZ)l(l —rDZ).] In terms of variance components, H consists
of:
H =
iV BG
W BG+ VWE
This coefficient can be seen to differ considerably from true
heritability:
V v ixrn + 1 V nn V
WO ' BG_______ _ _ Gr.
hr =
v + V + V + V V
W G ~ BG WE BE P
18. The significance of the difference between two Fs is tested by
transforming the Fs to a unit normal variate and referring the
difference to the normal distribution to determine its p value. The
appropriate transformation is given by Paulson (1942).
19. A simple approximation to the standard error of h2 as determined
by the twin method is given by Newman Freeman & Holzinger
(1937, p. 116):