r
has proved that the assumption is justified. Tests of the same
75 individuals with five different vocabulary tests of this type showed
that the average difference between two tests of the same person was
less than 5 per cent. This means that any one of the five tests used is
reliable enough for all practical purposes. It is of no special
importance that a given child's vocabulary is 8000 rather than 7600; the
significance lies in the fact that it is approximately 8000 and not
4000, 12,000, or some other widely different number.

It may seem to the reader almost incredible that so small a sampling of
words would give a reliable index of an individual's vocabulary. That it
does so is due to the operation of the ordinary laws of chance. It is
analogous to predicting the results of an election when only a small
proportion of the ballots have been counted. It is known that a ballot
box contains 600 votes, and if when only 30 have been counted it is
found that they are divided between two candidates in the proportion of
20 and 10, it is safe to predict that a complete count will give the two
candidates approximately 400 and 200 respectively.[61] In 1914 about
1,000,000 votes were cast for governor in California, and when only
10,000 votes had been counted, or a hundredth of all, it was announced
and conceded that Governor Johnson had been reelected by the 150,000
plurality. The completed count gave him 188,505 plurality. The error was
less than 4 per cent of the total vote.

[61] Supposing the ballots to have been shuffled.

The vocabulary test has a far higher value than any other single test of
the scale. Used with children of English-speaking parents (with children
whose home language is not English it is of course unreliable), it
probably has a higher value than any three other tests in the scale. Our
statistics show that in a large majority of cases the vocabulary test
alone will give us an intelligence quotient within 10 per cent of that
secured by the entire scale. Out of hundreds of English-speaking
children we have not found one testing significantly above age who had a
significantly low vocabulary; and correspondingly, those who test much
below age never have a high vocabulary.

Occasionally, however, a subject tests somewhat higher or lower in
vocabulary than the mental age would lead us to expect. This is often
the case with dull children in cultured homes and with very intelligent
children whose home enviro