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

Race Differences in Intelligence 195
NOTES
1. A critique of the SPSSI Council’s statement was published by
Jensen (1969c).
2. Obtained scores can be conceived of as analyzable into two components:
true-scores plus an error component. The reliability (rtt)
of a test is defined as the ratio of true score variance to obtained
score variance and the proportion of variance due to measurement
error, therefore, is 1 —rtt. Errors of measurement, being random,
cancel each other when scores are averaged to obtain a group mean.
Adding a random number (half of which are + and half —) to
each score in a distribution, where the number of scores is large,
will increase the variance of the distribution but will not significantly
alter the mean. On the other hand, when the absolute difference
(i.e., a difference regardless of its sign, + or —) between a pair
of scores is obtained, it includes the measurement error. For
example, imagine a set of many pairs of ‘true’ scores (i.e., scores
without any error) in which the scores of both members of each
pair are identical (although the mean of each pair may differ from
the mean of every other pair). The mean of the absolute differences
within pairs, therefore, will be zero. Now imagine adding random
numbers (i.e., error) to every individual score. Then the mean of
the absolute differences within pairs will be some value greater
than zero. This value constitutes measurement error.
3. The correlation between twins can be determined from the mean
absolute difference |d \ between twin pairs from the following
formula
where
\dk\ — mean absolute difference between kinship members,
|dp\ = mean absolute difference between all possible paired
comparisons in the general population, and
\ir\
M3«r
Since the population o for IQ is 15, and the twin difference is 6-60,
the above formula yields a value for r = 0-85. Thus, if the genetic
variance for IQ = 0-85 x 152 = 191-25, and the error variance is
(1—r t)er2 [where rn is test reliability] = (—1-95)152 = 11-25, and
the total variance is 152 = 225, then the environmental variance
(i.e., the remainder) must equal 22-50, which has a standard