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 correlat- 
ing 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 situa- 
tion 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 circum- 
stances 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 abil- 
ities involved in both performances. 
Statistical devices for determining the relationship be- 
tween test and criterion are of two sorts. One of these de- 
vices, used when the criterion or both the criterion and the 
test scores are discrete variables, tells how much the differ- 
ent 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- 
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