Page 145 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH

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

Notes
1 ⎧ ⎛ W H ⎞ 1
⎟
(iv) In P = 2 ⎩ ⎨⎜ ⎝ R − H K1 N – NR H +
C
− ⎠
H
⎛ W L ⎞ 1 ⎫
⎜ R L − ⎟ ⎬ the R denotes ______
− ⎠
⎝ K1 N – NR L ⎭ H
L
(a) Number of candidates in top group giving right response
(b) Number of candidates in top group giving wrong response
(c) Number of total candidates in top group
(d) Number of total candidates in bottom group

R – R – 1
H
L
(v) Difficulty percentage = R1 − R L is called
T
N − NR T
T
(a) Guilford formula
(b) Chi-square test formula
(c) Kelly’s formula
(d) 27% Top and 27% bottom right response method
10.7 The Discrimination Index

The ‘Discrimination Index’ is a basic measure which shows the extent to which a question
discriminates or differentiates between students in the ‘High Marks’ group and ‘Low Marks’
group. This index can be interpreted as an indication of the extent to which overall knowledge of
the content area or mastery of the skills is related to the response on an item. Most crucial for a
test item is that whether a student got a question correct or not is due to their level of knowledge
or ability and not due to something else such as chance or test bias.
Note in our example earlier, 11 students in the high group and 2 students in the low group
selected the correct answer. This indicates positive discrimination, since he item differentiates
between students in the same way that the total test score does. That is, students with high scores
on the test (high group) got the item right more frequently than students with low scores on the
test (low group). Although analysis by inspection may be all that is necessary for most purposes,
an index of discrimination can be easily computed using the following formula :
Discrimination Index =
Number of Students in ‘High Marks’ group (R ) with the Correct Answer u) Minus (—)
H
Number of Students in ‘Low Marks’ group (R ) with the Correct Answer divided by (÷)
L
Half the Total Number of Students who Attempted the Question (½T)
Example : A test was given to a group of 43 students and 10 out of the 13 ‘High Marks’ group got
the correct answer compared to 5 out of 13 ‘Low Marks’ group who got the correct answer. The
discrimination index is computer as follows :

−
−
R − R 10 5 10 5
= H L = = = 0.38
½T ( ½26 ) 13
What does a Discrimination Index of 0.38 mean ? The discrimination index is a coefficient that
shows the extent to which the question discriminates or differentiates between ‘High Marks”

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