Page 141 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH

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

Notes
⎛ 60 ⎞ 1
P = ⎜ 240 − ⎟ [W = N – R]
− ⎠
c ⎝ 41 300
⎛ 60 ⎞ 1
= ⎜ 240 − ⎟
⎝ 3300
⎠
= ( − )240 20 1
300

220
= = .733
300
= .733 × 100 = 73.3% (Difficulty Index in Percent)
Sometimes it is seen in multiple choice items that a student is not able to attempt some items of
the test. It could be due to lack of time or the items being very difficult, or some other cause. Such
items are called unattempted or unreached items. For explanation, supposing in a 50-item test, a
candidate has attempted all questions from 1 to 25, he has not attempted items 26 and 27, and
then he has solved all items from 28 to 40, and has not solved any item after that. In such a
situation, items 41 to 50 will be called unattempted or unreached items, but not items 26 and 27.
besides, there will be three groups of candidates : who have given right responses, who have
given wrong responses and who have not responded.
In solving this type of questions, the formula is amended to the following form :

⎛ W ⎞ 1
P = ⎜ R − ⎟
− ⎠
− ⎝
c K1 N NR
Here, NR is the number of candidates who have not been able to solve an item or have not
attempted it. The remaining all symbols have been used as in the previous formula.
Example : Supposing, a 100-item test was administered to 300 candidates. Each item contained 4
alternatives. This is also assumed that 150 were right responses, 120 were wrong responses and
30 were unattempted. In such a situation, the difficulty index of that particular item will be as
follows:
⎛ 120 ⎞ 1
P = ⎜ 150 − ⎟
− ⎝
− ⎠
c 41 300 30
⎛ 120 ⎞ 1
= ⎜ 150 − ⎟
⎝ 3 ⎠ 270

= ( − )150 40 1
270

1
= 110×
270

11
=
27
= 0.4 ×100
= 40%

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