o a larger
number of decimal places than the original measures would justify. Final
results should usually not be refined far beyond the accuracy of the
original measures.

It is of utmost importance in calculating medians and other measures of
a distribution to keep constantly in mind the significance of each step
on the scale. If the scale consists of tasks to be done or problems to
be solved, then "doing 1 task correctly" means, when considered as part
of a continuous scale, anywhere from doing 1.0 up to doing 2.0 tasks. A
child receives credit for "2 problems correct" whether he has just
barely solved 2.0 problems or has just barely fallen short of solving
3.0 problems. If, however, the scale consists of a series of productions
graduated in quality from very poor to very good, with which series
other productions of the same sort are to be compared, then each sample
on the scale stands at the middle of its "step" rather than at the
beginning.

The second kind of scale described in the foregoing paragraph may be
designated as "scales for the _quality_ of products," while the other
variety may be called "scales for _magnitude_ of achievement." In the
one case, the child makes the best production he can and measures its
quality by comparing it with similar products of known quality on the
scale. Composition, handwriting, and drawing scales are good examples of
scales for quality of products. In the other case, the scales are placed
in the hands of the child at the very beginning, and the magnitude of
his achievement is measured by the difficulty or number of tasks
accomplished successfully in a given time. Spelling, arithmetic,
reading, language, geography, and history tests are examples of scales
for quantity of achievement.

Scores tend to be more accurate on the scales for magnitude of
achievement, because the judgment of the examiner is likely to be more
accurate in deciding whether a response is correct or incorrect than it
is in deciding how much quality a given product contains. This does not
furnish an excuse for failing to employ the quality-of-products scales,
however, for the qualities they measure are not measurable in terms of
the magnitude of tasks performed. The fact appears, however, that the
method of employing the quality-of-products scales is "by comparison"
(of child's production with samples reproduced on the scale), while the
method of employing the magnitude-of-achievement scales is "by
perfor