After a group of tests has been given and each test has been
rated, the result is a collection of ratings which is often very
confusing. It is quite necessary, from every point of view, to
be able to express all these ratings in terms of a single rating
for the entire group. This is sometimes done by adding to
gether the results in each test, a procedure which is obviously
fallacious, because each test may have a different value.
The value of each test is determined by its index of correla
tion. The tests for inspectors, for instance, were found to have
correlations of plus .56 for 2, plus .63 for 6, and plus .72 for 8.
Therefore, test 8 should be given more weight in the final result
than 6, etc. The proportional value of each test may be approxi
mately found by dividing each correlation by the sum of all the
correlations. In the above instance this gives .30 for 2, .32 for
6, and .38 for 8. That is, test 2 is to count 30% of the total,
test 6, 32%, and test 8, 38%, no matter what the record in
each test is.
Pro-rating is the process of applying a formula by which the
rating in a group of tests can be combined in such a way as to
give each rating its proportional value in the final result. If
we use the results of the above analysis, and apply it to the
inspectors’ test, we shall have the following formula:
.30 X 2r + .32 X 6r + .38 X 8r = R, in which R is the final
group rating, and 2r, 6r, and 8r the rating in each of the three
tests. If our deduction has been correct, R should be 1.00
when each test has been done in reference time. E. g., .30 X 1.00
+ .32 X 1.00 + .38 X 1.00 = 1.00.
It is impossible to apply this formula to any ratings which
are not computed on a standard basis similar to that described
under the section on rating.
It is also desirable to pro-rate tests in accordance with chang
ing and special conditions. For instance, in the case of clerical
tests, it may be necessary to place considerable emphasis on
the arithmetical test, especially for ledger, statistical, and ac
