Page 77 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH

Unit 6 : Validity – Types , Methods and Usability

make a rough prediction. From the standpoint of scoring, the students who solve the item Notes
correctly are given 1 mark and those who are not able to do so are given 0 mark. Thus, we have
only two classes, and the correlation calculated between these two is equal to r of Pearson
pbi
coefficient.
The value of r can be calculated by the use of a formula, which is as are as follows :
pbi
m − m
r pbi = p q ⋅ pq
σ
Where, M = Mean of the first group
p
M = Mean of the second group
q
p = Ratio of sample in the first group.
q = Ratio of sample in the second group.

σ 1 = Standard deviation of the entire group.
4. Tetrachoric Correlation : This method is used in such a situation when both variables X and Y
are dichotomous. If they are dichotomous, rbias cannot be calculated, and in their place,
tetrachoric correlation is calculated. In some appropriate conditions, the value of r comes equal
1
to Pearson (r). Therefore, r is supposed be approximation of Pearson (r).
1
The following formula is used to calculate this type of correlation :
⎧ ⎫
⎪ ⎪ 180 ⎪ ⎪
cos ⎨ ⎬
r = ad
1 ⎪ 1 + ⎪
⎪ ⎩ bc ⎪ ⎭
Here, a, b, c, d frequencies are arranged as per the following table
X-Variable

Y-Variable – + Total Porportions

+ – + + + a + b P
– –– + - c + d Q
Total b + d a + c 1.00
Proportions P’ Q’ 1.00

Both variables have been divided into two categories : X and Y. Cell A has + + entries and Cell
B has – –. If correlation is fully positive, then all cases will be set in a and d cells, and if
correlation is fully negative, all cases will be set in b and c cells. If frequencies are similar in all
four cells, then correlation will be zero. On applying the value of a, b, c, d in the formula, when
the bracket is opened, a number is received which is in the form of a fraction angle. The cos
value of this angle is found out. This value expresses the extent of r . When the value of ad is
t
more than bc, then the value of r will be positive and when the value of bc is more than ad,
t
then r will be negative. When the value of bc is equal to ad, then the value of the angle will be
t
90°, and the value of r will be equal to cos 90° or zero. When angle is 0°, then the value of r will
t t
be +1 and when it is 180°, then the value of r will be –1.
t
The values of more than cos 90° are not given in the table. When the angle is between 90° and
180°, then it is deducted from 180° and its cosine value is referred and the obtained value is
given the prior mark.
Tetrachoric correlation is found advantageous when we want to see the correlation between
two attributes, and it is not possible to measure these two variables in the form of scores, but

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