244 THE MISMEASURE OF MAN
students have taken more times than they care to remember.)
Statisticians are trained to be suspicious of distributions with
multiple modes. Such distributions usually indicate inhomogeneity
in the system, or, in plainer language, different causes for the dif-
ferent modes. All familiar proverbs about the inadvisibility of mix-
ing apples and oranges apply. The multiple modes should have
guided Yerkes to a suspicion that his tests were not measuring a
single entity called intelligence. Instead, his statisticians found a
way to redistribute zero scores in a manner favorable to hereditar-
ian assumptions (see next section).
Oh yes, was anyone wondering how my students fared? They
did very well of course. Anything else would have been shocking,
since all the tests are greatly simplified precursors of examinations
they have been taking all their lives. Of fifty-three students, thirty-
one scored A and sixteen B. Still, more than 10 percent (six of fifty-
three) scored at the intellectual borderline of C; by the standards
of some camps, they would have been fit only for the duties of a
buck private.
FINAGLING THE SUMMARY STATISTICS:
THE PROBLEM OF ZERO VALUES
If the Beta test faltered on the artifact of a secondary mode for
zero scores, the Alpha test became an unmitigated disaster for the
same reason, vastly intensified. The zero modes were pronounced
in Beta, but they never reached the height of the primary mode at
a middle value. But six of eight Alpha tests yielded their highest
mode at zero. (Only one had a normal distribution with a middle
mode, while the other yielded a zero mode lower than the middle
mode.) The zero mode often soared above all other values. In one
test, nearly 40 percent of all scores were zero (Fig. 5.7a). In
another, zero was the only common value, with a flat distribution
of other scores (at about one-fifth the level of zero values) until an
even decline began at high scores (Fig. 5.7b).
Again, the common-sense interpretation of numerous zeros
suggests that many men didn't understand the instructions and
that the tests were invalid on that account. Buried throughout
Yerkes's monograph are numerous statements proving that testers
worried greatly about the high frequency of zeros and, in the midst