Page 143 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH

Unit 10 : Item Analysis : Item Difficulty, Discrimination index, Effectiveness of Distractors

10.6.3 Calculation of D.P. Using Chi-square Test Formula Notes
When the values calculated by the above formulae are different, it presents difficulty in their
comparative study; therefore, another formula is applied which is called Chi-square test formula.
this formula has two forms. The first form is applied in the situation when the value of R is
H
more than R , and the second form is applied when the value of R is more than R .
L L H
H −R L − R 1
D.P. = R1 − R L (First form, when R > R );
T
N T − NR L H L
and

R H − R + L 1
⎛ R ⎞
D.P. = R T ⎜ 1 − T ⎟ (Second form when R > R )
L
H
⎝ N − NR T ⎠
T
Example : 340 class-10 students were administered a test. All related values of the test are given
below. Find out discriminating value using any square formula.
N = 100, R = 65, and NR = 15
H H H
N =100, R =25 and NR = 35
L L L
Solution : ∴ Discriminating Value :

R − H R − L 1
⎛ R ⎞
= R T ⎜ 1 − T ⎟
⎝ N − NR T ⎠
T
−
65 26 ⎧ ⎪ N=N + N L ⎫ ⎪
H
T
T
H
= 90 − ⎛ 1 − ⎜ 90 ⎞ ⎟ ⎨ R=R + R L ⎬
⎝ 200 50 ⎠ − ⎪ ⎩ NR =NR + NR L ⎭ ⎪
H
T
65 26
−
= 90 − ⎛ 1 − ⎜ 90 ⎞ ⎟
⎝ 200 50 ⎠ −
39
⎛
= 90 1 − 3 ⎞ ⎟
⎜
⎝ 5 ⎠

39
2
⎛⎞
= 90 ⎜⎟
⎝⎠
5
39
=
36

39
=
6
= 6.5
Therefore, D.P. = 6.5

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