Explains how reliability is calculated

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. Reliability
The word ‘reliable’ is generally used in day to
day life.
Is that person, ‘A’ reliable?
This means that, can we depend him/her. If A is
reliable, he/she will exhibit his/her set of
behaviours again and again. This makes that
person reliable.

3. Reliability
- concept
Reliability is Consistency or stability in
scores.
For example, a student ‘A’ gets 15 marks in
AL test yesterday. AL test is repeated after
two weeks. If ‘A’ got around 15 marks then,
the test is reliable otherwise the test is not
reliable.

4. Reliability
- concept
Which is reliable?
1
2

5. Reliability
- concept
1 is reliable
1
2

6. Reliability
- Types If same test is given after a period of time say, first
week of a month and then third week of that month
that is, Test Retest Reliability.
If two sets of question paper are prepared having
same blue print and administered to same samples
that is, Parallel forms

7. Reliability
- Types

8. Reliability
-
calculation
Reliability is calculated by correlation coefficient
(r). Before knowing about r, correlation should
be known.

9. Correlation
If the change in one variable appears to be
accompanied by a change in the other variable,
the two variables are said to be co-related and
this inter-dependence is called correlation

10. Changes
The influence of change in one variable on the
other can be of three types.
If the value of one variable increases, it may be
accompanied by increase in other variable, said
to be positive correlation.
If the value of one variable increases, it may be
accompanied by decrease in other variable,
said to be negative correlation.
If the value of one variable increases, it may be
accompanied by neither increase nor decrease
in other variable, said to be zero correlation.

11. Examples
Can you guess examples for three types of
correlation.

12. Examples
‘+’ correlation: Height and Weight, Intelligence
and Achievement.
‘-’ correlation: Pressure and Volume,
Happiness and Stress.
‘0’ correlation: Singing and Arithmetic.

13. Positive
Correlation

14. Negative
Correlation

15. Zero
Correlation

16. Correlation
Coefficient
(r)
Correlation coefficient is a number. It tells to
what extent the variations in one variable
changes with the variations in the other
Can you guess the range of correlation
coefficient?

17. Correlation
Coefficient
(r) - Range
Range: -1 to 0 to +1
Positive correlation to zero to negative
correlation

18. r - formula
There are different correlation coefficients like
rank order correlation coefficient, Product
moment correlation coefficient, Bi-serial
correlation coefficient etc. which depends
upon the type of data like nominal, ordinal,
ratio and interval.

19. r - formula
Here Product Moment Correlation Coefficient
is only explained and the data is of interval
type. Product moment correlation coefficient is
also known as by its inventor Karl Pearson
correlation coefficient.

20. r - formula

21. r – formula
Modified

22. r –
calculation
Having understood about the formula, now it
can be calculated. Let us take test retest
reliability. That is, now Test A will be conducted
to the same 10 students (X) and after 15 days
Test A administered to same set of students (Y).
Now we will be having two sets of data X and Y.
(Parallel form reliability also can be taken, but
we have to have two sets of question paper for
the same blue print)

23. r – Steps in
Calculation
1. Calculate mean for X scores
2. Calculate mean for Y scores
3. Calculate deviation (x) for each score (X)
from their respective mean
4. Calculate deviation (y) for each score (Y)
from their respective mean
5. Calculate xy
6. Calculate x2, Σx2
7. Calculate y2, Σy2

24. r – Step by
Step
1. Calculate mean for X scores
2. Calculate mean for Y scores

25. Marks of 10 Students taken test at two different time
S.NO. Test A Test B
S1 31 31
S2 32 32
S3 33 33
S4 34 34
S5 35 35
S6 36 36
S7 37 37
S8 38 38
S9 39 39
S10 40 40
Mean 35.5 35.5

26. r – Step by
step
3. Calculate deviation (x) for each score (X)
from their respective mean
4. Calculate deviation (y) for each score (Y)
from their respective mean

27. Marks of 10 Students taken test at two different time
S.NO. Test A Test B x = M-X y = M-Y
S1 31 31 4.5 4.5
S2 32 32 3.5 3.5
S3 33 33 2.5 2.5
S4 34 34 1.5 1.5
S5 35 35 0.5 0.5
S6 36 36 -0.5 -0.5
S7 37 37 -1.5 -1.5
S8 38 38 -2.5 -2.5
S9 39 39 -3.5 -3.5
S10 40 40 -4.5 -4.5
Mean 35.5 35.5

28. r – Steps in
Calculation
5. Calculate xy

29. Marks of 10 Students taken test at two different time
S.NO. Test A Test B x = M-X y = M-Y xy
S1 31 31 4.5 4.5 20.25
S2 32 32 3.5 3.5 12.25
S3 33 33 2.5 2.5 6.25
S4 34 34 1.5 1.5 2.25
S5 35 35 0.5 0.5 0.25
S6 36 36 -0.5 -0.5 0.25
S7 37 37 -1.5 -1.5 2.25
S8 38 38 -2.5 -2.5 6.25
S9 39 39 -3.5 -3.5 12.25
S10 40 40 -4.5 -4.5 20.25
Mean 35.5 35.5 Σxy=80.25

30. r – Steps in
Calculation
6. Calculate x2, Σx2
7. Calculate y2, Σy2

31. Marks of 10 Students taken test at two different time
S.NO. Test A Test B x = M-X y = M-Y xy x2
y2
S1 31 31 4.5 4.5 20.25 20.25 20.25
S2 32 32 3.5 3.5 12.25 12.25 12.25
S3 33 33 2.5 2.5 6.25 6.25 6.25
S4 34 34 1.5 1.5 2.25 2.25 2.25
S5 35 35 0.5 0.5 0.25 0.25 0.25
S6 36 36 -0.5 -0.5 0.25 0.25 0.25
S7 37 37 -1.5 -1.5 2.25 2.25 2.25
S8 38 38 -2.5 -2.5 6.25 6.25 6.25
S9 39 39 -3.5 -3.5 12.25 12.25 12.25
S10 40 40 -4.5 -4.5 20.25 20.25 20.25
Mean 35.5 35.5 Σxy=80.25 Σx2=80.25Σy2=80.25

32. r
r = Σxy/√ Σx2 Σy2
= 80.25 / √ 80.25x 80.25
= +1
(Caution: I have taken hypothetical values for the students)

33. Assessme
nt
✓ R=+1, it is highly correlated
✓ What decision can be taken with this value?

34. Judgment
S.No. Value Interpretation
1 + 1 Perfect Positive / Negative Correlation
2 +0.90 to + 0.99 Very High Positive / Negative Correlation
3 + 0.70 to + 0.90 High Positive / Negative Correlation
4 + 0.50 to + 0.70 Moderate Positive / Negative Correlation
5 + 0.30 to + 0.50 Low Positive / Negative Correlation
6 + 0.10 to + 0.30 Very Low Positive / Negative Correlation
7 + 0.00 to + 0.10 Insignificant Positive / Negative Correlation

35. Implications
✓ Based on the table in previous slide, one has
to select the reliable questions and reject the
unreliable questions.
✓ r value which is equal to or more than +0.7
are reliable questions.
✓ Our set of questions are selected.

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

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

38. 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.
✓ Highly reliable questions are selected.

39. Assignment
✓ Based on the previous slides, have
hypothetical marks for ten students on two
different occasions. Calculate r and take final
decision whether to accept or reject the
questions.
✓ (For Remembrance: for pilot study 100
students have to be taken. Here for practice
we are taking 10 students)

40. 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