Page 79 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH

Unit 6 : Validity – Types , Methods and Usability

X Y Notes
Vocabulary Test 25% Grade Agerage

Now, supposing college students are also administered the intelligence test in addition to the
vocabulary test, and the correlation between intelligence test and grade average is .5 and 0 by
the vocabulary test. The intelligence test explains 25% variation of average variance. Thus,
vocabulary and intelligence tests explain 50% variance together.
X Y X
2
Vocabulary Test 25% Grade Agerage 25% Intelligence Test

This joint variance which is described by predictor tests, is used in calculating correlation
coefficient. This variance is equal to the square of multiple correlation. In this examination, the
value of multiple correlation will be equal to .50 or .71, and it will be displayed by R . In its full
123
form, following is the formula for multiple correlation :
R
1.234.....n
This symbol displays correlation of all tests 2, 3, 4,.... with test-l.
Thus, if we link several tests in the test battery, whose mutual correlation is zero and they are
correlated with the criterion, then multiple correlation will be equal to the total sum of squares
of the correlation of criteria of predictors, that is :
R 2 ...n = r 2 + r 2 +.....+ r 2
1.23 1.2 1.3 1.n
General Definition of Multiple Correlation :
“Multiple correlation is the correlation between scores on one variable and the composite
scores on several other tests while these scores are optimally weighted.”
Table : Semesters Completed in Percents
Decile 2 3 4 5 6 7 8

X 97 94 93 91 89 88 86
VII 93 86 84 80 78 77 77
VI 91 81 78 76 72 71 71
II 84 70 65 63 60 58 57
I 80 66 57 50 49 48 45

It is clear here that the students who are given X item (maximum), there is possibility that 70%
students will complete the semester; while in the lowest decile group, there are only 45% students
who will be able to pass the semester.
Prediction can also be displayed by another method, called bar diagram. By it, the predictive
ability of a test is calculated. Under this, a test battery which has been used for selecting workers
for pilot training, the percentage of students on stanine has been displayed. It is clear from it
that on the basis of test, the individuals who obtain 9 stanine are least likely to be discharged
th
from their work (only about 4% pilots were discharged due to inefficiency), while those obtaining
1 stanine, 70% of them were discharged due to inefficiency. Thus, explanation can be given on
st
the basis of other stanines.
7. Cut-off Score Method : Cut-off score is a test score which is used as the demarcation point for
accepting or rejecting students. For example, supposing the following scores indicate adjustment
in some adjustment list, and we consider 9 as the cut-off score, then it would mean that the
students who have scored 9 or less on the adjustment inventory will be accepted, and those

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