This document provides information about performing a paired t-test, including the steps and an example. A paired t-test is used to compare two related samples, such as pre-test and post-test scores from the same group. The steps are: formulate hypotheses, determine if the test is one-tailed or two-tailed, calculate the degrees of freedom, select the t-test, compute the test statistic, state the decision rule based on critical value, and make a conclusion. An example tests if a new diet significantly reduces weight by comparing weights before and after for 7 women.

1. APPLICATION OF
HYPOTHESIS
TESTING

2. Steps in hypothesis
testing

3. Statistical Tests
T TEST OF
INDEPENDENT
MEANS
*Compare scores of
2 different variables
but for two different
groups of cases
T TEST OF
DEPENDENT
MEANS
(PAIRED T-
TEST)
*Compare scores of
2 different variables
but for the same
group of cases

4. Statistical Tests
T TEST OF
INDEPENDENT
MEANS
Example:
Comparing Math Anxiety
scores of BS Math
Female and Male
Students
T TEST OF
DEPENDENT
MEANS
(PAIRED T-
TEST)
Example:
Comparing Science
Anxiety scores of BSEd
Math Students before
and after joining a
seminar about anxiety

5. T test of Dependent
Means
When to use this test?
In some research designs, it is necessary to
measure a certain variable of the same
people more than once
Commonly used to test improvements (or
decrements) of performance over a period of
time
Use to show differences in the two (2)
measures coming from the same group

6. T test of Dependent
Means
If we want to find out if the
difference between paired
observations is significant
or not, use this test.

7.  
1
n
D
D
n
D
t
2
2

 



 D = sum of the differences between
the paired observations
2
D
 = sum of the squared difference
n = number of paired observation
T test of Dependent
Means

8. An investigator is interested in
assessing the effect of a film on the
attitude of students toward a certain
issue. A sample of five students is
administered an attitude scale before
and after viewing the film.
The before and after scores
are as follows:
Sample Problem 1

9. Sample
Before
Viewing
After
Viewing
Student 1 16 20
Student 2 7 27
Student 3 19 32
Student 4 11 33
Student 5 8 14
At 0.05 level of significance did the film
affect the attitude of the students?

10. T test of Dependent
Means
Step 1: Formulate the
Hypotheses
The film does not significantly affect the
attitude of the students.
The film significantly affects the attitude
of the students.

11. T test of Dependent
Means
Two-tailed (non-directional)
Step 3: Determine whether two-
tailed or one-tailed.

12. T test of Dependent
Means
Step 4: Compute the degrees
of freedom and determine the
critical value/tabular value

14. T table comes
in different
format but the
process is still
the same.

15. T test of Dependent
Means
Step 5: Select the appropriate
statistical test and compute
for test statistic.
For this, the statistical test to be used is T test of
Dependent Means.
 
1
n
D
D
n
D
t
2
2

 




16. 65
D 


Sample
Before
Viewing
After
Viewing
D D2
1 16 20 -4 16
2 7 27 -20 400
3 19 32 -13 169
4 11 33 -22 484
5 8 14 -6 36
Sample
Before
Viewing
After
Viewing
D D2
1 16 20
2 7 27
3 19 32
4 11 33
5 8 14
Sample
Before
Viewing
After
Viewing
1 16 20
2 7 27
3 19 32
4 11 33
5 8 14
1105
D2


T test of Dependent
Means

17. 605
.
3


t
 
1
n
D
D
n
D
t
2
2

 



   
1
5
65
1105
5
65
t
2





T test of Dependent
Means
Step 5: Compute for test
statistic.

18. T test of Dependent
Means
Step 6: State the decision
rule.

19. T test of Dependent
Means
Step 6: State the decision
rule.
CRITICAL VALUE

20. T test of Dependent
Means
Step 6: State the decision
rule.
3.605

21. T test of Dependent
Means
Step 7: Make a conclusion.

22. It is claimed that a new diet will
reduce a person’s weight by 10
pounds on the average in a period of
2 weeks. The weights of 7 women
who followed this diet were recorded
before and after a 2-week period.
Sample Problem 1

23. Woman
Weight
Before
Weight
After
1 129 130
2 133 121
3 136 128
4 152 137
5 141 129
6 138 132
7 125 120
Test the claim of the manufacturer
at 0.05 level of significance.

24. T test of Dependent
Means
Step 1: Formulate the
Hypotheses
The new diet did not significantly reduce a
person’s weight.
The new diet significantly reduced a
person’s weight.

25. T test of Dependent
Means
One-tailed (directional)
Step 3: Determine whether two-
tailed or one-tailed.

26. T test of Dependent
Means
Step 4: Compute the degrees
of freedom and determine the
critical value/tabular value

28. T test of Dependent
Means
Step 5: Select the appropriate
statistical test and compute
for test statistic.
For this, the statistical test to be used is T test of
Dependent Means.
 
1
n
D
D
n
D
t
2
2

 




29. 57
D 
 639
D2


Woman X Y D D2
1 129 130 -1 1
2 133 121 12 144
3 136 128 8 64
4 152 137 15 225
5 141 129 12 144
6 138 132 6 36
7 125 120 5 25
Woman X Y D D2
1 129 130
2 133 121
3 136 128
4 152 137
5 141 129
6 138 132
7 125 120
Woman X Y
1 129 130
2 133 121
3 136 128
4 152 137
5 141 129
6 138 132
7 125 120
T test of Dependent
Means

30. 99
.
3
t 
 
1
n
D
D
n
D
t
2
2

 



   
1
7
57
639
7
57
t
2



T test of Dependent
Means
Step 5: Compute for test
statistic.

31. T test of Dependent
Means
Step 6: State the decision
rule.

32. T test of Dependent
Means
Step 6: State the decision
rule.
CRITICAL VALUE

33. T test of Dependent
Means
Step 6: State the decision
rule.
3.99

34. T test of Dependent
Means
Step 7: Make a conclusion.

36. A training director of a large chain of
department stores in Makati wants to
know if a weeks training course will help
12 salesladies’ rapport with the
customers. One month prior to the
training and one month after training
there were rated in a 10 point scale. At
0.05 level of significance is there a
reason to believe that the training has
improved the rapport of salesladies with
the customers.

37. Sample Before the
Training
After the
Training
1 6.9 7.0
2 6.9 7.1
3 7.2 8.3
4 6.8 7.0
5 6.5 6.6
6 6.0 6.0
7 5.3 5.6
8 7.0 7.7
9 6.6 7.0
10 6.8 6.8
11 6.3 6.3
12 5.2 5.3