UMT, Test Construction 2, Test Construction II, Item Analysis, Test Analysis, Test Construction, Discrimination Index, Difficulty Index, Waqas A. Khan, Prof. Dr. Abdul Hameed, Abdul Hameed, Dr. Abdul Hameed, SSH, University of Management and Technology, University of Management & Technology, www.waqas.org

1. BY: PROF. DR. ABDUL HAMEED
ITEM ANALYSIS
A PRACTICAL APPROACH
WAQAS A. KHAN

2. ABOUT THE INSTRUCTOR
• Mr. Waqas A. Khan is a PhD Scholar in Educational Assessment
& Evaluation at the University of Management & Technology
Lahore.
• He holds M.Phil degree in Quality Management, M.Ed and
diploma in “Practical Project Management” from Ateneo De
Manila University Philippines. He is a Certified Lead Auditor in
ISO 9001:2008 Quality Management System.
• Currently he is working as Director, Hazara Public School &
College Changa Manga.
For Details: www.waqas.org | www.hazara.edu.pk

3. ITEM ANALYSIS: WHY?
Are the items reliable? Do they
measure consistently?
What items are most difficult to
answer correctly?
What items are easy?
Are there any poor performing
items that need to be discarded?

4. OBJECTIVES
1. Assess quality of the distractors.
2. Assess difficulty of the items.
3. Assess how well an item
differentiates between high and
low performers.
4. Assess Reliability of the test.

5. TEST DATA
ITEM ANALYSIS
Paper English Class 9th Boys
TOTAL QUESTIONS: 19
TOTAL STUDENTS: 39
Paper Syllabus: 1st Half Book
HAZARA PUBLIC SCHOOL &
COLLEGE CHANGA MANGA
(KASUR)
WWW.HAZARA.EDU.PK

6. STEP 1
Students - Questions
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
1
C
B
A
B
A
B
D
C
C
C
A
B
C
B
B
B
C
A
19
B
2
C
C
B
C
C
B
D
C
A
A
C
C
C
B
B
B
C
C
C
3
C
B
A
C
C
B
D
C
A
C
C
D
C
B
B
C
B
C
C
4
B
B
A
A
B
C
D
C
A
A
A
A
B
A
B
A
A
D
5
C
B
B
B
D
B
D
C
C
A
A
D
C
C
B
B
D
6
C
B
B
C
D
B
D
C
B
C
A
D
B
A
B
B
C
C
C
7
C
B
B
D
B
D
C
C
A
D
A
A
B
B
C
B
C
8
C
B
A
B
C
B
D
C
D
C
A
D
A
B
B
B
C
C
D
9
A
C
D
C
C
B
D
C
D
C
A
B
C
A
B
B
C
C
D
10
D
B
B
C
A
B
D
C
D
A
B
B
C
D
C
B
A
C
B
11
C
B
B
C
C
B
D
C
A
D
C
A
C
A
B
C
C
B
A
12
C
B
B
B
A
B
D
C
D
D
A
D
D
C
B
B
C
B
A
13
C
B
A
B
A
B
B
C
D
D
A
D
D
B
B
B
C
A
A
14
C
D
B
B
D
B
D
C
A
A
D
A
D
C
B
B
C
B
C
C
15
B
D
A
A
C
B
B
C
C
A
B
C
C
B
A
C
B
B
A
16
D
C
D
A
D
A
D
C
B
A
D
A
C
A
A
B
A
C
C
17
C
B
C
A
D
B
D
C
D
A
A
D
B
B
C
A
C
C
D
18
C
B
A
D
C
B
D
C
A
D
A
D
B
A
C
A
B
19
C
B
A
B
C
B
D
C
C
C
A
D
C
B
B
B
C
D
20
C
B
B
B
C
B
D
C
A
C
A
D
B
D
B
A
B
C
D
21
C
B
A
A
D
B
D
C
D
A
A
D
D
C
B
B
C
C
A
22
C
B
B
B
C
B
D
C
A
C
C
D
A
A
B
B
C
A
C
23
C
B
A
A
C
B
B
C
A
C
A
B
A
D
B
C
D
C
D
24
C
B
C
C
B
D
C
D
A
C
C
A
C
D
B
C
C
B
25
C
B
B
A
B
D
C
C
D
A
D
A
C
D
C
C
A
B
26
B
B
D
C
A
B
C
C
B
A
A
B
A
B
B
D
C
D
27
C
B
D
C
C
B
C
C
B
C
C
D
B
C
A
28
B
B
B
A
A
C
A
B
C
C
A
C
B
B
C
B
B
D
C
29
C
B
A
C
C
B
D
C
A
C
C
D
C
A
B
C
B
D
C
30
B
A
D
B
A
C
A
D
B
C
A
C
A
A
B
B
C
D
C
31
C
B
D
D
B
D
C
A
C
32
B
D
D
A
C
B
D
C
D
A
C
A
B
B
B
C
A
C
B
33
C
B
A
B
A
B
D
C
D
C
A
B
C
C
B
B
C
D
34
C
B
B
C
D
B
D
C
D
C
A
D
B
A
B
B
C
B
35
C
B
B
B
A
B
D
C
D
C
A
D
A
A
B
B
C
A
D
36
C
B
B
C
D
B
D
C
B
C
A
D
B
B
B
B
C
B
C
37
C
B
B
C
D
B
D
C
A
C
A
D
C
A
B
B
C
B
C
38
C
B
A
C
C
B
D
C
D
C
A
D
D
B
B
B
C
A
A
39
C
B
B
C
C
D
D
C
A
C
C
D
C
A
B
C
C
C
C
B
C
C
In Excel Sheet
write Question
Numbers in
Columns and
Student
Numbers in
Rows. Fill the
response of
each student
against each
question. i-e
(A,B,C or D)

7. STEP 2
A
B
C
D
1
1
12
7
10
1
1
1
11
13
25
7
9
14
3
3
4
8
6
5
31
15
14
0
36
3
0
6
2
2
7
8
11
31
26
5
8
6
30
3
1
15
17
1
4
36
6
19
9
4
15
9
2
9
26
17
16
2
3
6
2
12
1
31
2
13
5
2
21
5
3
2
0
4
3
9
In this step we shall check that against each question how many A, B,
C and D have been ticked by the students.
For this the formula is
= COUNTIF(C3:C41, "A")
• C3 and C41 is the range of rows in which we have entered the
response data. You can change this according to your range of
data.
• “A” will be changed to “B”, “C” and “D” accordingly.

8. STEP 3
A
2.564 2.564 30.77 17.95 25.64 2.564 2.564 2.564 28.21 33.33 64.1 17.95 23.08 35.9 7.692 7.692 10.26 20.51 15.38
B
12.82 79.49 38.46 35.9
C
D
0
92.31 7.692
0
15.38 5.128 5.128 17.95 20.51 28.21 79.49 66.67 12.82 20.51 15.38
76.92 7.692 2.564 38.46 43.59 2.564 10.26 92.31 15.38 48.72 23.08 10.26 38.46 23.08 5.128 23.08 66.67 43.59 41.03
5.128 7.692 15.38 5.128 30.77 2.564 79.49 5.128 33.33 12.82 5.128 53.85 12.82 7.692 5.128
0
10.26 7.692 23.08
We will now find out the percentage of A,B,C and D responses against
each question. In this example, total students are 39. So we shall divide
each cell with 39 and multiply it with 100 to find the percentage
responses.
For this the formula is
=(C47/39)*100
• C47 is the cell address. 39 is the number of total students and 100 is
for %.
Cross Check 97.44 97.44 87.18 97.44 100
100
100
100 92.31 100 97.44 100 94.87 94.87 97.44 97.44 100 92.31 94.87
• For cross Checking that we are going right, we can add the four
columns and our result shall be 100 or very near to it (EXP)

9. STEP 4
KEY:
C
B
B
C
A
B
D
C
D
C
A
D
A
A
B
B
C
B
C
• Now we shall put the right answers in one row. “KEY”
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
11
2
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
10
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
10
6
11
15
15
13
11
9
11
14
11
10
3
5
9
9
10
10
11
14
8
10
10
9
10
5
11
9
6
5
12
17
16
15
16
13
12
After putting in the “KEY”
we shall now ask the
computer to mark the
student according to the
key now. For every right
answer the mark given is
1and 0 for vice versa.
Formula to do this is
=IF(C3="C",1,0)
* We are directing
computer to mark every C
in Q1 as 1 and others 0. In
next column replace C
with the right KEY ANSWER
and paste down.

10. STEP 5
34
35
37
6
7
36
12
22
8
38
33
39
1
5
9
11
13
21
29
2
3
14
19
20
24
25
27
10
17
18
26
30
23
4
31
16
28
32
15
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
17
16
16
15
15
15
14
14
13
13
12
12
11
11
11
11
11
11
11
10
10
10
10
10
10
10
10
9
9
9
9
9
8
6
6
5
5
5
3
Now we shall arrange the
obtained marks in
“Descending Order”
The purpose of doing this
is that we want to arrange
the obtained marks of the
class on the quantum of
ability i-e
High Achievers (Ph)
Low Achievers (Pl)
This will help us in
measuring difficulty and
discrimination ahead.

11. PH AND PL
Ph
Pl
1
0.3
1
0.5
0.7
0.1
0.5
0.1
0.2
0.3
1
0.8
1
0.4
1
0.7
0.5
0.1
0.9
0.2
0.9
0.5
1
0.1
0.4
0.3
0.6
0.3
1
0.6
1
0.5
1
0.3
0.5
0.1
0.6
0.3
14.8
6.5
• Now we shall find out the top 25% and bottom 25%
for this the way is:
Total number of students : 39, 25% of 39 is about 10.
• So we will sum the obtained marks of top 10 and
bottom 10 students and shall divide this sum with
number of these students i-e 10.
Formula to do this is.
Formula Ph: =SUM(C116:C125)/10
Formula Pl: =SUM(C145:C154)/10

12. DISCRIMINATION & DIFFICULTY
Discrimination
0.7
0.5
0.6
0.4
-0.1
0.2
0.6
0.3
0.4
0.7
0.4
0.9
0.1
0.3
0.4
0.5
0.7
0.4
0.3
• For Discrimination value, we shall subtract Ph from Pl.
Difficulty
0.769 0.795 0.385 0.385 0.256 0.923 0.795 0.923 0.333 0.487 0.641 0.538 0.231 0.359 0.795 0.667 0.667 0.205 0.41
• For Difficulty we shall add obtained marks in each
question and divide it with total number of students.
Formula :
Discrimination: = (C160-C161)
Difficulty: =SUM(C116:C154)/39

13. RELIABILITY
To find reliability, we shall now paste the obtained marks
data into SPSS Software.

14. RELIABILITY
Click Analyze
Then Click on Scale
Click on Reliability
Analysis
You will find this
answer
Case Processing Summary
N
Cases
Valid
%
39
a
Excluded
Total
100.0
0
0.0
39
100.0
a. Listwise deletion based on all variables in
the procedure.
Reliability Statistics
Cronbach
's Alpha N of Items
.689
19

15. ANALYSIS
RELIABILITY INDEX DESIRED VALUE 0.8 and >

16. DECISION
Item
Diff.
Disc.
No.
Index
Index
1
2
3
4
5
0.8
0.8
0.4
0.4
0.7
0.5
0.6
0.4
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0.3
0.9
0.8
0.9
0.3
0.5
0.6
0.5
0.2
0.4
0.8
0.7
0.7
0.2
0.4
-0.1
0.2
0.6
0.3
0.4
0.7
0.4
0.9
0.1
0.3
0.4
0.5
0.7
0.4
0.3
Distracter Effect %
A
B
C
D
Decisio
n
3
3
31
18
13
79*
38*
36
77*
8
3
38*
5
8
15
5
26*
0
44
31
3
3
92*
8
3
10
3
79*
3
0
92*
5
28
33
64*
18
23*
36*
8
8
10
21
15
15
5
5
18
21
28
79*
67*
13
21*
15
15
49*
23
10
38
23
5
23
67*
44
41*
33*
13
5
54*
13
8
5
0
10
8
23
Select
Select
Select
Select
Reject
(B)
Reject
Select
Reject
(B)
Select
Select
Select
Select
Reject
Select
Select
Select
Select
Select
Select

17. QUESTIONS?
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