VALIDATION OF MEASURING INSTRUMEN TS 169
this formula should not be used in place of the uncorrected
value in predicting one variable from another.
Better correction for attenuation is obtained by correlating
 both sets of test scores and criterion records. The
formula then becomes
a Mri
Still more refined correction is possible if each set of test
scores Is correlated with each of the sets of criterion records
(233, p. 213):
(£) Toy w= Vr Tog, Tra - Pro ® Try
V Tez, * Ty,
Validity. Each test or other measuring instrument must
be evaluated by making a statistical comparison between the
scores of the subjects and their vocational accomplishment.
The concomitance of these two variables can be determined
accurately and stated mathematically. From this observed
relationship may then be inferred the predictive value of the
tests under similar future conditions. In the practical situation
 the test score is always the known variable, and the
vocational success the predicted variable.
The reason for the relationship between the two variables
is a matter of interesting speculation. Unless special circumstances
 or weaknesses in the experiment allow extraneous
forces to account for the relationship, it may be assumed
with reasonable assurance that the relation between the two
variables is caused by some common ability or group of abilities
 involved in both performances.
Statistical devices for determining the relationship between
 test and criterion are of two sorts. One of these devices,
 used when the criterion or both the criterion and the
test scores are discrete variables, tells how much the different
 classes of vocational success, represented by their central
tendencies, differ in test performance. Such a device gives
an expression of the significance of the difference found be-)