tive correlation is
indicated by the number + 1, perfect negative correlation by the
number - 1, and zero correlation by 0. A correlation of +.8 indicates
close positive correspondence, though not perfect correspondence; a
correlation of +.3 means a rather low, but still positive,
correspondence; a correlation of -.6 means a moderate tendency towards
inverse relationship.

The correlation between two good intelligence tests, such as the Binet
and the Alpha, comes out at about +.8, which means that if a fair
sample of the general population, ranging from low to high
intelligence, is given both tests, the order of the individuals as
measured by the one test will agree pretty closely with the order
obtained with the other test. The correlation between a general
intelligence test and a test for mechanical ability is considerably
lower but still positive, coming to about +.4. Few if any real
negative correlations are found between different abilities, but low
positive or approximately zero correlations are frequent between
different, rather special abilities.

In other words, there is no evidence of any antagonism between
different sorts of ability, but there is plenty of evidence that
different special abilities may have little or nothing in common.

[Footnote]
Possibly some readers would like to see a sample of the
statistical formulae by which correlation is measured. Here is one
of the simplest. Number the individuals tested in their order as
given by the first test, and again in their order as given by the
second test, and find the difference between each individual's two
rank numbers. If an individual who ranks no. 5 in one test ranks no.
12 in the other, the difference in his rank numbers is 7. Designate
this difference by the letter D. and the whole number of individuals
tested by n. Square each D, and get the sum of all the squares,
calling this sum "sum of D2[squared]". Then the correlation is given
by the formula,

1 - ( ( 6 X sum of D[squared] ) / (n x ( n[squared] - 1)) )

As an example in the use of this formula, take the following:

Individuals Rank of each Rank of each D D[squared]
tested individual in individual in
first test second test

Albert 3 5 2 4

George 7 6 1 1

Henry 5 3 2 4

Jam