The Mismeasure of Man by Stephen Jay Gould

THE MISMEASURE OF MAN

from one battery to another and has no fundamental psychological signif-

icance beyond the arbitrary collection of tests that anyone happens to put

together.... We cannot be interested in a general factor which is only the

average of any random collection of tests.

Burt had identified group factors by looking for clusters of pos-
itive and negative projections on the second and subsequent prin-
cipal components. Thurstone objected strenuously to this method,
not on mathematical grounds, but because he felt that tests could
not have negative projections upon real "things." If a factor rep-
resented a true vector of mind, then an individual test might either
measure that entity in part, and have a positive projection upon
the factor, or it might not measure it at all, and have a zero projec-
tion. But a test could not have a negative projection upon a real
vector of mind:

A negative entry. .. would have to be interpreted to mean that the

possession of an ability has a detrimental effect on the test performance.

One can readily understand how the possession of a certain ability can aid

6*10 Thurstone's illustration of how the position of the first principal
component (the x in both figures) is affected by the types of tests included
in a battery.