illustrates the calculation of discrimination index

1. Reliability – Test Retest, Parallel Forms
Discrimination Index
Difficulty Index
Pilot Study
Scoring Key
Setting Question Paper
Writing Questions
Blue Print
Weightage to Type of Questions
Weightage to Contents
Weightage to Objectives

2. Discrimination
Index
(Dis.I)

3. Dis.I -
Definiti
on
What does the name suggest?
An index that discriminates.
Discriminates what?
Dis.I is the ability of the question to differentiate
between performers from non-performers.

4. Dis.I -
Formula
NH-NL
Dis.I = --------
NT
Where
NH- Number of students answered
correctly in high group
NL - Number of students answered
correctly in low group
NT - Total Number of students in high
or low group

5. Dis.I – Steps
in
Calculation
1. Calculate total marks for each student
2. Arrange them in descending order
3. Make top 27% as high group
4. Make bottom 27% as low group
5. Find who has answered correctly for a
particular question in high (NH) and low
group (NL)
6. Calculate Dis.I

6. Dis.I -
Calculati
on
✓ Dis.I will have to be calculated for each
question.
✓ You remember that we have taken 10
students for calculating DI. Now also we
are taking the same scores of 10 students
for the calculation of Dis.I.
✓ Caution: To make it easier for
understanding purpose we have taken 10
students otherwise normally, Pilot Study
should be done with 100 students.

7. Dis.I – Steps
in
Calculation
1. Calculate total marks for each student

8. Marks of 10 Students’ for Q1-Q15
Q.NO. S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 0 1 0 1
3 0 1 1 1 1 0 0 1 0 1
4 1 0 1 1 0 0 1 1 1 1
5 1 1 1 1 1 1 1 1 0 0
6 1 1 1 1 1 1 1 1 1 1
7 1 1 1 1 1 1 1 1 1 1
8 0 0 1 0 0 1 0 1 1 0
9 1 1 0 0 1 0 1 0 1 1
10 0 1 0 1 1 1 1 0 1 1
11 1 1 1 1 1 0 0 1 0 1
12 1 1 1 0 0 1 1 1 1 0
13 1 1 0 1 1 1 1 0 1 1
14 1 1 1 1 1 1 1 1 1 1
15 0 0 1 0 1 0 0 1 1 1

9. Marks of 10 Students’ for Q16-Q29 and Sum
Q.NO. S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
16 1 1 1 1 1 1 1 1 0 1
17 1 0 0 1 1 1 0 1 0 1
18 1 1 1 1 1 1 1 1 0 0
19 1 1 1 0 0 1 1 0 1 1
20 0 1 1 1 1 0 1 0 1 1
21 2 2 2.5 2.5 2 2 2 2.5 2 2
22 1.5 1.5 2 1.5 1.5 2 2.5 2 1.5 2.5
23 3 3 3 3 3 3 3 3 3 3
24 2.5 2 2 2.5 2 1.5 2 1.5 2 2
25 3 2 2.5 2 1.5 2 2.5 2.5 2 2
26 4 3 3.5 3 2.5 2 3.5 4 4.5 4
27 3 3 4 3 5 3 5 3 3 4
28 4 4 4 3 4 3 4 4 4 4
29 0 0 0 0 0 0 0 0 0 0
Sum 38 36.5 39.5 35.5 37.5 32.5 38.5 37.5 35 39.5

10. Dis.I – Steps
in
Calculation
2. Arrange them in descending order

11. Descending Order of Total Marks
Stud. Sum
S10 39.5
S3 39.5
S7 38.5
S1 38
S5 37.5
S8 37.5
S2 36.5
S4 35.5
S9 35
S6 32.5

12. Dis.I – Steps
in
Calculation
3. Make top 27% as high group
4. Make bottom 27% as low group
Since we have taken 10 students 27% of 10 is
2.7 ≈ 3. So, Top 3 students will make the high
group and bottom 3 students will make the
low group

13. High and Low groups
Sum
S10 39.5
S3 39.5
S7 38.5
S1 38
S5 37.5
S8 37.5
S2 36.5
S4 35.5
S9 35
S6 32.5
High
Group
Low
Group

14. Dis.I – Steps
in
Calculation
5. Find who has answered correctly for a
particular question in high (NH) and low
group (NL)
6. Calculate Dis.I
✓ We have to take only the scores of
students who fall in high and low group.

15. Dis.I –
Objective
Questions
✓ From Q1 to Q20, it is objective questions. After
that it is subjective questions. For objective
questions if the answer is correct, the mark is 1
and if it is wrong, the mark is 0. This is not the
case for Q21 to Q29. How to calculate Dis.I for
that?

16. Dis.I for
subjective
question
✓ This can be handled easily like this. If the mark is
more than 70% for a question then it is considered as
1 otherwise 0.
✓ For example, let us take Q21. The maximum marks is
3 and 70% of 3 is 2.1≈2. Hence if a student gets 2 or
more marks, it is taken as 1 and if he/she gets less
than 2 marks, it is taken as 0.
✓ For Q26, the maximum marks is 5 and 70% of 5 is 3.5.
Hence if a student gets 3.5 or more marks, it is taken
as 1 and if he/she gets less than 3.5 marks, it is taken
as 0.
✓ Now it can be calculated.

17. Dis.I for Q1-Q15
Q.NO. S10 S3 S7 S4 S9 S6 NH NL NT Dis.I
1 1 1 1 1 1 1 3 3 3 0
2 1 1 0 1 0 1 2 2 3 0
3 1 1 0 1 0 0 2 1 3 0.34
4 1 1 1 1 1 0 3 2 3 0.34
5 0 1 1 1 0 1 2 2 3 0
6 1 1 1 1 1 1 3 3 3 0
7 1 1 1 1 1 1 3 3 3 0
8 0 1 0 0 1 1 1 2 3 -0.34
9 1 0 1 0 1 0 2 1 3 0.34
10 1 0 1 1 1 1 2 3 3 -0.34
11 1 1 0 1 0 0 2 1 3 0.34
12 0 1 1 0 1 1 2 2 3 0
13 1 0 1 1 1 1 2 3 3 -0.34
14 1 1 1 1 1 1 3 3 3 0
15 1 1 0 0 1 0 3 3 3 0

18. Disfor Q16-Q29 and Sum
Q.NO. S10 S3 S7 S4 S9 S6 NH NL NT Dis.I
16 1 1 1 1 0 1 3 2 3 0.34
17 1 0 0 1 0 1 1 2 3 -0.34
18 0 1 1 1 0 1 2 2 3 0
19 1 1 1 0 1 1 3 2 3 0.34
20 1 1 1 1 1 0 3 2 3 0.34
21 2 2.5 2 2.5 2 2 3 3 3 0
22 2.5 2 2.5 1.5 1.5 2 3 1 3 0.67
23 3 3 3 3 3 3 3 3 3 0
24 2 2 2 2.5 2 1.5 3 2 3 0.34
25 2 2.5 2.5 2 2 2 3 3 3 0
26 4 3.5 3.5 3 4.5 2 3 2 3 0.34
27 4 4 5 3 3 3 3 0 3 1
28 4 4 4 3 4 3 3 1 3 0.67
29 0 0 0 0 0 0
Sum 39.5 39.5 38.5 35.5 35 32.5

19. Dis.I –
Calculati
on for
Q1
NH-NL 3 -3
Dis.I = -------- = --- = 0
NT 3

20. Dis.I –
Calculati
on for
Q8
NH-NL 1-2
Dis.I = -------- = --- = -0.34
NT 3

21. Dis.I –
Calculati
on for
Q21
NH-NL 3-3
Dis.I = -------- = --- = 0
NT 3

22. Dis.I –
Calculati
on for
Q26
NH-NL 3-2
Dis.I = -------- = --- = 0.34
NT 3
Remember Q29, which is a choice question is not
attempted by any of the students. Hence, Dis.I was
unable to be calculated

23. Dis.I -
Relationship
✓ What is the proportionality between
Dis.I and discrimination of a question?
✓ Directly proportional.
✓ If Dis.I is high then, discrimination is
high. This means that the question
which has high Dis.I discriminates high
with low performer markedly.

24. DI -
Range
✓ What is the range of Dis.I.
✓ Think of three cases.
1. All students in high group answered correctly
and no one in low group answered correctly
2. No one in high group answered correctly and all
students in low group answered correctly
3. All students in high and low groups answered
correctly

25. DI -
Range
✓ It is -1 to +1.
✓ Case 1: Dis.I = 3-0/3 = 1
✓ Case 2: Dis.I = 0-3/3 = -1
✓ Case 3: Dis.I = 0-0/3 = 0

26. Assessme
nt
✓ After calculation of Dis.I, you will come to know
that which question discriminates the students
markedly and which do not.
✓ What do you think to be done with the Dis.I
value?

27. Assessme
nt
✓ We need the questions which discriminates
high and low performer (high discriminating
power) and do need not the questions which
does not discriminates high and low performer.

28. Judgment

29. Implications
✓ Based on the table in previous slide, one has
to select excellent and good questions and
reject the fair and poor question.

30. Decision
Q.NO. Dis.I Decision
1 0 REJ
2 0 REJ
3 0.34 SEL
4 0.34 SEL
5 0 REJ
6 0 REJ
7 0 REJ
8 -0.34 REJ
9 0.34 SEL
10 -0.34 REJ
11 0.34 SEL
12 0 REJ
13 -0.34 REJ
14 0 REJ
15 0 REJ
Q.NO. Dis.I Decision
16 0.34 SEL
17 -0.34 REJ
18 0 REJ
19 0.34 SEL
20 0.34 SEL
21 0 REJ
22 0.67 SEL
23 0 REJ
24 0.34 SEL
25 0 REJ
26 0.34 SEL
27 1 SEL
28 0.67 SEL
Don’t Worry. This
many will not get
rejected in reality.
This is model only. If a
question is
constructed as per
criteria, rejection will
be less.

31. Final
Decision
✓ For a particular question to be selected, both
DI and Dis.I should be in the selection range,
otherwise it will be rejected.

32. Final Decision
Q.NO D.I Dis.I Decision
1 1 0 REJ
2 0.8 0 REJ
3 0.6 0.34 SEL
4 0.7 0.34 SEL
5 0.8 0 REJ
6 1 0 REJ
7 1 0 REJ
8 0.4 -0.34 REJ
9 0.6 0.34 SEL
10 0.7 -0.34 REJ
11 0.7 0.34 SEL
12 0.7 0 REJ
13 0.8 -0.34 REJ
14 1 0 REJ
15 0.5 0 REJ
Q.NO. D.I Dis.I
Decisi
on
16 0.9 0.34 SEL
17 0.6 -0.34 REJ
18 0.8 0 REJ
19 0.7 0.34 SEL
20 0.7 0.34 SEL
21 1 0 REJ
22 0.5 0.67 SEL
23 1 0 REJ
24 0.8 0.34 REJ
25 0.9 0 REJ
26 0.6 0.34 SEL
27 0.5 1 SEL
28 0.8 0.67 REJ
If a question is
selected, it is
selected in both
DI and Dis.I. Red
colored fonts,
are selected in
one index and
rejected in other,
but overall
decision is
rejected.

33. Implications
✓ If some questions are rejected what is to be
done?

34. Implications
✓ Again write the question, go for pilot study,
calculate new DI and Dis.I and based on it
select or reject the question.

35. For
Understanding
✓ Very Easy and highly difficult questions are to
be avoided. Only moderate questions are to
be kept in the question paper.
✓ Questions with high discriminating power
are kept in the question paper.

36. Assignment
✓ Based on the previous slides, have
hypothetical marks for all questions for ten
students. Calculate Dis.I and take final
decision whether to accept or reject the
questions by combining DI and Dis.I.

37. References
• Mathew, T.K., and Mollykutty, T.M. (2011). Science Education -Theoretical bases
of teaching and pedagogic analysis - Physical Science and Natural Science.
Kerala: Rainbow Book Publishers
• NCERT. (2013). Teaching of science. Delhi: Author
• Radha Mohan. (2007). Teaching of physical science. (3rd ed.). Delhi: PHI Learning
• Rathinasabapathy, P. (2001). கல்வியில் தேர்வு [Examination in Education].
(2nd ed.). Chennai: Shantha Publishers.
• Srinivasan, P. (2011). அறிவியல் கற்பிே்ேல் [Teaching of science].
Thanjavur: DDE, Tamil Univeristy
• Images from google