338 THE MISMEASURE OF MAN
"out there" in fixed positions within a factorial space. He argued
that Spearman and Burt's factors were not "real" because they var-
ied in number and position among different batteries of tests.
Spearman retorted that Thurstone's PMA's were also artifacts of
chosen tests, not invariant vectors of mind. A PMA could be cre-
ated simply by constructing a series of redundant tests that would
measure the same thing several times, and establish a tight cluster
of vectors. Similarly, any PMA could be dispersed by reducing or
eliminating the tests that measure it. PMA's are not invariant loca-
tions present before anyone ever invented tests to identify them;
they are products of the tests themselves:
We are led to the view that group factors, far from constituting a small
number of sharply cut "primary" abilities, are endless in number, indefi-
nitely varying in scope, and even unstable in existence. Any constitutent of
ability can become a group factor. Any can cease being so (1939, p. 15).
Spearman had reason to complain. Two years later, for exam-
ple, Thurstone found a new PMA that he could not interpret (in
Thurstone and Thurstone, 1941). He called it Xi and identified it
by strong correlations between three tests that involved the count-
ing of dots. He even admitted that he would have missed Xi
entirely, had his battery included but one test of dotting:
All these tests have a factor in common; but since the three dot-count-
ing tests are practically isolated from the rest of the battery and without
any saturation on the number factor, we have very little to suggest the
nature of the factor. It is, no doubt, the sort of function that would ordi-
narily be lost in the specific variance of the tests if only one of these dot-
counting tests had been included in the battery (Thurstone and Thur-
stone, 1941, pp. 23-24).
Thurstone's attachment to reification blinded him to an obvious
alternative. He assumed that Xx really existed and that he had pre-
viously missed it by never including enough tests for its recogni-
tion. But suppose that Xx is a creation of the tests, now "discovered"
only because three redundant measures yield a cluster of vectors
(and a potential PMA), whereas one different test can only be
viewed as an oddball.
There is a general flaw in Thurstone's argument that PMA's
are not test-dependent, and that the same factors will appear in
any properly constituted battery. Thurstone claimed that an indi-