This document discusses how to calculate the difficulty index and discrimination index of test items to evaluate their quality. The difficulty index is the ratio of students who answered correctly to the total students. It ranges from 0 to 1, with values below 0.25 or above 0.75 indicating an item needs revision. The discrimination index measures how well items distinguish between top and bottom scoring groups, ranging from -1 to 1. Values below -0.5 mean the item should be discarded. The document provides examples of calculating both indexes and determining the appropriate action for each item based on the index values.

2. ITEM
ANALYSIS
-Edward John B. Daluz, LPT

3. DIFFICULTY INDEX
measures the difficulty level of a test item.
ratio of the number of students who got the correct
answer with respect to the class population
𝑠𝑢𝑏𝑡𝑜𝑡𝑎𝑙
𝑔𝑟𝑎𝑛𝑑 𝑡𝑜𝑡𝑎𝑙
=
𝑛𝑜. 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑤ℎ𝑜 𝑔𝑜𝑡 𝑡ℎ𝑒 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑎𝑛𝑠𝑤𝑒𝑟
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠

4. DIFFICULTY INDEX
Range of
Difficulty Index
Interpretation Action
0 – 0.25 Difficult Revise/discard
0.26 – 0.75
Right difficulty/
moderately difficult
Retain
0.76 – 1 Easy Revise/discard

5. In test item 1 (one) of the
mathematics 7 final exam, 7 students
answered A, 14 answered B, 11
answered C, and 3 answered D.
Considering that the correct answer
is letter B, what should the teacher
do with the test item?
Sample Problems (I DO)

6. A B C D TOTAL
7 14 11 3
Sample Problems (I DO)
A B C D TOTAL
7 14 11 3
A B C D TOTAL
7 14 11 3 35
𝑛𝑜. 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑤ℎ𝑜 𝑔𝑜𝑡 𝑡ℎ𝑒 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑎𝑛𝑠𝑤𝑒𝑟
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
14
35
= 0.40

7. Range of
Difficulty Index
Interpretation Action
0 – 0.25 Difficult Revise/discard
0.26 – 0.75
Right difficulty/
moderately difficult
Retain
0.76 – 1 Easy Revise/discard
Range of
Difficulty Index
Interpretation Action
0 – 0.25 Difficult Revise/discard
0.40 0.26 – 0.75
Right difficulty/
moderately difficult
Retain
0.76 – 1 Easy Revise/discard
Sample Problems (I DO)

8. In test item 1 (one) of the
mathematics 7 final exam, 7 students
answered A, 14 answered B, 11
answered C, and 3 answered D.
Considering that the correct answer
is letter C, what should the teacher
do with the test item?
Sample Problems (WE DO)

9. A B C D TOTAL
7 14 11 3
Sample Problems (WE DO)
A B C D TOTAL
7 14 11 3
A B C D TOTAL
7 14 11 3 35
𝑛𝑜. 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑤ℎ𝑜 𝑔𝑜𝑡 𝑡ℎ𝑒 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑎𝑛𝑠𝑤𝑒𝑟
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
11
35
= 0.31

10. Range of
Difficulty Index
Interpretation Action
0 – 0.25 Difficult Revise/discard
0.26 – 0.75
Right difficulty/
moderately difficult
Retain
0.76 – 1 Easy Revise/discard
Range of
Difficulty Index
Interpretation Action
0 – 0.25 Difficult Revise/discard
0.31 0.26 – 0.75
Right difficulty/
moderately difficult
Retain
0.76 – 1 Easy Revise/discard
Sample Problems (WE DO)

11. In test item 1 (one) of the
mathematics 7 final exam, 7 students
answered A, 14 answered B, 11
answered C, and 3 answered D.
Considering that the correct answer
is letter A, what should the teacher
do with the test item?
Sample Problems (YOU DO)

12. A B C D TOTAL
7 14 11 3
Sample Problems (YOU DO)
A B C D TOTAL
7 14 11 3
A B C D TOTAL
7 14 11 3 35
𝑛𝑜. 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑤ℎ𝑜 𝑔𝑜𝑡 𝑡ℎ𝑒 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑎𝑛𝑠𝑤𝑒𝑟
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
7
35
= 0.20

13. Range of
Difficulty Index
Interpretation Action
0 – 0.25 Difficult Revise/discard
0.26 – 0.75
Right difficulty/
moderately difficult
Retain
0.76 – 1 Easy Revise/discard
Range of
Difficulty Index
Interpretation Action
0.20 0 – 0.25 Difficult Revise/discard
0.26 – 0.75
Right difficulty/
moderately difficult
Retain
0.76 – 1 Easy Revise/discard
Sample Problems (YOU DO)

14. DISCRIMINATION INDEX
Measures how well can the items distinguish
between the upper groups and lower groups.
𝐷𝑈 − 𝐷𝐿
DU – the difficulty index of the upper 25%
DL – the difficulty index of the lower 25%

15. X = total number of
takers
(0.25X) = upper 25% of
the takers
(0.25X) = lower 25% of
the takers
(0.50X) = middle 50%
of the takers

16. X = total number of
takers
(0.25X) = upper 25% of the takers
(0.25X) = lower 25% of the takers

17. X = 40
(0.25X) = 0.25 (40)
upper 25% of the takers = 10
(0.25X) = 0.25 (40)
lower 25% of the takers = 10
upper 25% = rank 1-10
upper 25% = rank 31-40

18. X = 100
(0.25X) = 0.25 (100)
upper 25% of the takers = 25
(0.25X) = 0.25 (100)
lower 25% of the takers = 25
upper 25% = rank 1-25
upper 25% = rank 76-100

19. DISCRIMINATION INDEX
Index Range Interpretation Action
(-1.00) – (-0.50)
Negative
discrimination index
discard
(-0.49) – (0.45) Non-discriminating revise
(0.46) – (1.00)
Positive discrimination
index
retain

20. Sample Problems
A B C D TOTAL
Whole
Class
15 40 20 25 100
Upper
25%
8 13 2 2
25
(1-25)
Lower
25%
1 11 4 9
25
(76-100)
20/100 = 0.20 (difficult) revise/discard

21. Sample Problems
Upper
25%
8 13 2 2
25
(1-25)
Lower
25%
1 11 4 9
25
(76-100)
𝐃𝐔 − 𝐃𝐋 =
𝟐
𝟐𝟓
−
𝟒
𝟐𝟓
−
𝟐
𝟐𝟓
𝐃𝐔 − 𝐃𝐋 =
−𝟎. 𝟎𝟖
𝐃𝐔 − 𝐃𝐋 =

22. DISCRIMINATION INDEX
Index Range Interpretation Action
(-1.00) – (-0.50)
Negative
discrimination index
discard
(-0.49) – (0.45) Non-discriminating revise
(0.46) – (1.00)
Positive discrimination
index
retain
Index Range Interpretation Action
(-1.00) – (-0.50)
Negative
discrimination index
discard
-0.08 (-0.49) – (0.45) Non-discriminating revise
(0.46) – (1.00)
Positive discrimination
index
retain

23. Sample Problems
A B C D TOTAL
Whole
Class
15 40 20 25 100
Upper
25%
8 13 2 2
25
(1-25)
Lower
25%
1 11 4 9
25
(76-100)
25/100 = 0.25 (difficult) revise/discard

24. Sample Problems
Upper
25%
8 13 2 2
25
(1-25)
Lower
25%
1 11 4 9
25
(76-100)
𝐃𝐔 − 𝐃𝐋 =
𝟐
𝟐𝟓
−
𝟗
𝟐𝟓
−
𝟕
𝟐𝟓
𝐃𝐔 − 𝐃𝐋 =
−𝟎. 𝟐𝟖
𝐃𝐔 − 𝐃𝐋 =

25. DISCRIMINATION INDEX
Index Range Interpretation Action
(-1.00) – (-0.50)
Negative
discrimination index
discard
(-0.49) – (0.45) Non-discriminating revise
(0.46) – (1.00)
Positive discrimination
index
retain
Index Range Interpretation Action
(-1.00) – (-0.50)
Negative
discrimination index
discard
-0.28 (-0.49) – (0.45) Non-discriminating revise
(0.46) – (1.00)
Positive discrimination
index
retain

26. Sample Problems
A B C D TOTAL
Whole
Class
15 40 20 25 100
Upper
25%
8 13 2 2
25
(1-25)
Lower
25%
1 11 4 9
25
(76-100)
15/100 = 0.15 (difficult) revise/discard

27. Sample Problems
Upper
25%
8 13 2 2
25
(1-25)
Lower
25%
1 11 4 9
25
(76-100)
𝐃𝐔 − 𝐃𝐋 =
𝟖
𝟐𝟓
−
𝟏
𝟐𝟓
𝟕
𝟐𝟓
𝐃𝐔 − 𝐃𝐋 =
𝟎. 𝟐𝟖
𝐃𝐔 − 𝐃𝐋 =

28. DISCRIMINATION INDEX
Index Range Interpretation Action
(-1.00) – (-0.50)
Negative
discrimination index
discard
(-0.49) – (0.45) Non-discriminating revise
(0.46) – (1.00)
Positive discrimination
index
retain
Index Range Interpretation Action
(-1.00) – (-0.50)
Negative
discrimination index
discard
0.28 (-0.49) – (0.45) Non-discriminating revise
(0.46) – (1.00)
Positive discrimination
index
retain

29. I. Identify the difficulty index of the following test items.
1. 13 out of 40 students got the answers INCORRECTLY.
2. 24 out of 50 students got the answers correctly.
3. 17 and 33 students got the incorrect and correct answers
respectively.
II. Identify the final action to be taken regarding the test item
with the data below. (show all necessary solutions)
A B C D TOTAL
Whole Class 24 16 33 27
Upper 25% 2 6 12 5
Lower 25% 14 4 3 4
ASSIGNMENT