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

114 Educability and Group Differences
a negative correlation. Often genetic and environmental hypotheses
of subpopulation differences lead to the same predictions so that
one cannot decide between them on the basis of empirical outcomes.
But here we have a situation in which environmental and
genetic hypotheses predict diametrically opposite outcomes.
Using the data of Table 4.1 (omitting height and weight), we
can determine the correlation between E' and W~Njaw. The mean
white-Negro difference must be divided by the standard deviation
in the white sample (aw) in order to express all the differences on
the same scale for the various tests. The differences are thus
expressed in white sigma units.6 Figure 4.1 shows the scatter
diagram relating W-NjGw (the Y axis) and E' = |rs —0*501 (the
X axis). The white samples are plotted as white triangles and the
Negro samples as black triangles. The two bivariate means are
indicated by white and black circles. The regression lines for the
regression of Y on X are shown for both the white and Negro
groups. The regression line for whites has a somewhat steeper
slope than for Negroes. But in both cases the slope is negative,
which is opposite to the prediction from the environmental
hypothesis. The Pearson r between W-Njaw and E' = |rs —0*50 [
is —0*80 for whites and —0*61 for Negroes. The correlation
between the Negro and white values of E' is 0*71. This r of 0-71
means that the various tests are quite similar for whites and Negroes
in the degree to which they reflect non-genetic factors. (Since the
reliabilities of all these tests are quite uniformly high and about
the same for Negroes and whites, corrections for attenuation would
have a negligible effect on the results.)
Since extreme values on either the X or Y axis can inflate the
Pearson r, it is desirable to obtain a measure of correlation which
is free of the effects of scale and cannot be spuriously inflated by
extreme values. Spearman’s rank order correlation (rho) provides
this measure. For whites rho is —0-56 and for Negroes rho is
—0-47. The rho between white and Negro E' values is 0-64.
The most extreme values on both X and Y variables are those
of tests H 1 and #2, the Making Xs Test, which is not a cognitive
test but a motor skills test and was intended largely to reflect
test-taking motivation and effort. It is known to be sensitive to
instructions and situational factors and so it is not surprising that
it should show the highest E' index. We should also determine
the correlations when these two tests are eliminated, to make sure