Page 147 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH

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

Notes
P − P
D = 1 2
PQ 1 + P Q 2
2
1
N 1 N 2
In this formula, D means discriminating value. If this value is more than 1.96, then we can say
that our items are discriminating, that is, they are good enough to discriminate between good
and weak students. Thus, we calculate the discriminating value for each item. The items having
D higher than 1.96 or 2.00 will be considered as good.
The following formula is used to estimate the discriminating value of the test :
D.P. = PQ
Where, D.P. = Discriminating value
P = Number of students solving items correctly (in percent)

Q = The number of students solving items incorrectly (in percent)
Example : In a test, 50 students have solved an item correctly and the remaining incorrectly.
Estimate discriminating value of the item when the test was administered on 80 students.
Formula, D.P. = PQ

R
Here, P = × 100
N

50
= × 100
80
= 62.5%
W
And, Q = 100 – P [or Q = × 100 ]
N
= 100 – 62.5

= 37.5 percent
Thus, D.P. = 37.5 × 62.5
= 2343.5 (about)
[Note : An item with 2500 discriminating value is considered suitable.]
4.27% Top and 27% Bottom Right Response Method : This is a very popular method and it was
mentioned by Garrett in this way.
Under this method, the answer books are arranged in the descending order, that is, the answer
book obtaining the highest marks is placed at the top and the one obtaining the lowest marks is
placed at the bottom. Then the top 27% and bottom 27% are allowed to be the while the remaining
answer books are taken out. Supposing, we had a total of 300 answer books, then the top 81 and
bottom 81 answer books are taken while other 138 answer books are not considered. Now the
top and bottom groups are analyzed for the right responses for each item and their percentage is
found out. Then the difficulty index and bi-serial correlation, that is, discriminating value is
calculated using the table given on the previous page.
The use of table can be explained by the following example :
Example : In an examination, the number of candidates in the top 27% and bottom 27% solving
the first three of the eighty questions is as follows :

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