The Mismeasure of Man by Stephen Jay Gould

THE REAL ERROR OF CYRIL BURT

mathematically equivalent; neither is "better." Information is nei-
ther gained nor lost by rotating axes; it is merely redistributed.
Preferences depend upon the meaning assigned to factor axes.
The first principal component demonstrably exists. For Spearman,
it is to be cherished as a measure of innate general intelligence. For
Thurstone, it is a meaningless average of an arbitrary battery of
tests, devoid of psychological significance, and calculated only as an
intermediary step in rotation to simple structure.
Not all sets of vectors have a definable "simple structure." A
random array without clusters cannot be fit by a set of factors, each
with a few high projections and a larger number of near zero pro-
jections. The discovery of a simple structure implies that vectors
are grouped into clusters, and that clusters are relatively independ-
ent of each other. Thurstone continually found simple structure
among vectors of mental tests and therefore proclaimed that the
tests measure a small number of independent "primary mental
abilities," or vectors of mind—a return, in a sense, to an older "fac-
ulty psychology" that viewed the mind as a congeries of independ-
ent abilities.

Now it happens, over and over again, that when a factor matrix is

found with a very large number of zero entries, the negative entries dis-

appear at the same time. It does not seem as if all this could happen by

chance. The reason is probably to be found in the underlying distinct men-

tal processes that are involved in the different tasks.... These are what I

have called primary mental abilities (1940, p. 194).

Thurstone believed that he had discovered real mental entities

with fixed geometric positions. The primary mental abilities (or

PMA's as he called them) do not shift their position or change their

number in different batteries of tests. The verbal PMA exists in its

designated spot whether it is measured by just three tests in one

battery, or by twenty-five different tests in another.

The factorial methods have for their object to isolate the primary abil-

ities by objective experimental procedures so that it may be a question of

fact how many abilities are represented in a set of tasks (1938, p. 1).

ing clusters. In fact, it arose historically with reference to a definite theory of intelli-

gence (Thurstone's belief in independent primary mental abilities) and in

opposition to another (general intelligence and hierarchy of lesser factors) but-

tressed by principal components.