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

Step 3 : Multiply 45 (the number of answer sheets) with 0.27 (or 27%) which is 12.15 and Notes
rounded up to 12. The use of the value 0.27 or 27% is not inflexible. It is possible
to use any percentage between 27% to 35% as the value.
Step 4 : Arrange the pile of 45 answer sheets according to scores obtained (highest score
to the lowest score). Take out 12 answer sheets from the top of the pile and 12
answer sheets from the bottom of the pile. Call these two piles as “high marks”
students and “low marks” students. Set aside the middle group of papers (21
papers). Although these could be included in the analysis, using only the high
and low groups simplifies the procedure.
Step 5 : Refer to Item # 1 or Question # 1,
• Count the number of students from the “high marks” group who selected each of the
options (A, B, C and D),
• Count the number of students from the “low marks” group who selected the options
A, B, C or D.

Question 1 : Geography Test
What is the fertile area in the desert in which the water reaches the ground surface called ?
A. mirage
B. oasis
C. water hole

D. polder
Item Analysis
Options A B © D Blank
High Marks Group (n = 12) 0 11 1 0 0
Low Marks Group (n = 12) 3 2 3 4 0

Table 10.1 Item Analysis for One Item or Question
From the analysis, 11 students from the “High Marks” group and 2 students from the “Low
Marks” group selected ‘B’ which is the correct answer. This means that 13 out of the 24 students
selected the correct answer. Also, note that all the distractors; A, C, & D) were selected by at least
one student. However, the information provided in Figure 8.1 is insufficient and further analysis
has to be conducted.

10.4 The Difficulty Index

Using the information provided in you can compute the ‘Difficulty Index’ which is a quantitative
indicator with regards to the difficulty level of an individual item or question. It can be calculated
using the following formula :
()
Number of Students with the Correct Answer R
Difficulty Index = Total number of Students who Attempted the Question T
()

R 13
= = = 0.54
T 24
What does a Difficulty Index (p) of 0.54 mean ? The difficulty index is a coefficient that shows the
percentage of students who got the correct answer compared to the total number of students in

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