246 THE MISMEASURE OF MANof giving the tests, tended to interpret zeros in this common-sense
fashion. They eliminated some tests from the Beta repertoire (p.
372) because they produced up to 30.7 percent zero scores
(although some Alpha tests with a higher frequency of zeros were
retained). They reduced the difficulty of initial items in several
tests "in order to reduce the number of zero scores" (p. 341). They
included among the criteria for acceptance of a test within the Beta
repertoire (p. 373): "ease of demonstration, as shown by low per-
centage of zero scores." They acknowledged several times that a
high frequency of zeros reflected poor explanation, not stupidity
of the recruits: "The large number of zero scores, even with offi-
cers, indicates that the instructions were unsatisfactory" (p. 340).
"The main burden of the early reports was to the effect that the
most difficult task was 'getting the idea across.' A high percentage
of zero scores in any given test was considered an indication of
failure to 'get that test across' " (p. 379).
With all these acknowledgments, one might have anticipated
Boring's decision either to exclude zeros from the summary statis-
tics or to correct for them by assuming that most recruits would
have scored some points if they had understood what they were
supposed to do. Instead, Boring "corrected" zero scores in the
opposite way, and actually demoted many of them into a negative
range.
Boring began with the same hereditarian assumption that inval-
idated all the results: that the tests, by definition, measure innate
intelligence. The clump of zeros must therefore be made up of
men who were too stupid to do any items. Is it fair to give them all
zero? After all, some must have been just barely too stupid, and
their zero is a fair score. But other dullards must have been rescued
from an even worse fate by the minimum of zero. They would have
done even more poorly if the test had included enough easy items
to make distinctions among the zero scores. Boring distinguished
between a true "mathematical zero," an intrinsic minimum that
cannot logically go lower, and a "psychological zero," an arbitrary
beginning defined by a particular test. (As a general statement,
Boring makes a sound point. In the particular context of the army
tests, it is absurd):
A score of zero, therefore, does not mean no ability at all; it does not mean
the point of discontinuance of the thing measured; it means the point of
discontinuance of the instrument of measurement, the test.... The indi-