e of those who show
themselves to be more capable than the ordinary pupils.

The type of measurement which we wish to discuss is something more than
the ordinary examination. The difficulties with examinations, as we have
commonly organized them, has* been their unreliability, either from the
standpoint of discovering to us the deficiencies of children, or their
achievements. Of ten problems in arithmetic or of twenty words in
spelling given in the ordinary examination, there are very great
differences in difficulty. We do not have an adequate measure of the
achievements of children when we assign to each of the problems or words
a value of ten or of five per cent and proceed to determine the mark to
be given on the examination paper. If we are wise in setting our
examinations, we usually give one problem or one word which we expect
practically everybody to be able to get right. On the other hand, if we
really measure the achievements of children, we must give some problems
or some words that are too hard for any one to get right. Otherwise, we
do not know the limit or extent of ability possessed by the abler
pupils. It is safe to say that in many examinations one question may
actually be four or five times as hard as some other to which an equal
value is assigned.

Another difficulty that we have to meet in the ordinary examination is
the variability among teachers in marking papers. We do not commonly
assign the same values to the same result. Indeed, if a set of papers is
given to a group of capable teachers and marked as conscientiously as
may be by each of them, it is not uncommon to find a variation among the
marks assigned to the same paper which may be as great as twenty-five
per cent of the highest mark given. Even more interesting is the fact
that upon re-marking these same papers individual teachers will vary
from their own first mark by almost as great an amount.

Still another difficulty with the ordinary examination is the tendency
among teachers to derive their standards of achievement from the group
itself, rather than from any objective standard by which all are
measured. It is possible, for example, for children in English
composition to write very poorly for their grade and still to find the
teacher giving relatively high marks to those who happen to belong to
the upper group in the class. As a result of the establishment of such a
standard, the teacher may not be conscious of the fact that children