Statistical Test
DEPENDENT
SAMPLE T-TEST
BASAS, Quisha Mae
REAZO, Kay Darlyn
BOMBITA, Lleycon Christopher B.
Dependent Sample t-Test
Definition
When to use
Step by Step Procedure
Dependent
Sample t-Test
The dependent sample t-test , sometimes called the paired sample t-test , is a
statistical procedure used to determine whether the mean difference between
two sets of observations is zero. In a paired sample t-test, each subject or entity is
measured twice, resulting in pairs of observations.
Dependent
Sample t-Test
When do we used the Dependent Sample t-Test?
The dependent sample t-test is used when the observations or cases in one
sample are linked with the cases in the other sample. This is typically the case
when repeated measures are taken, or when analyzing similar units or
comparable specimen.
Dependent
Sample t-Test
Example Problem :
6 Grade 12 student are selected to attend a lecture about Statistical Mathematics and given a
30 item test before and right after the said lecture.
Hypotheses:
Ho : There is no significant difference in the pre-test and post-test of Statistical
Mathematics scores
Ha : There is significant difference in the pre-test and post-test of Statistical
Mathematics scores
Dependent
Sample t-Test
Data
Pre-test Scores
Post-test Scores
12
23
10
25
7
21
15
27
5
18
10
22
Dependent
Sample t-Test
Step by step procedure in computing Dependent Sample t-Test
Step 1 : Compute for the
Mean of the two
conditions
Pre-test Scores
Post-test Scores
12
23
10
25
7
21
15
27
5
18
10
22
M₁ = 9.83
M₂ = 22.6
Step 2 : Compute for the
Difference Scores
Total
Pre-test
Scores
Post-test
Scores
Difference
Difference
²
12
23
-11
121
10
25
-15
225
7
21
-14
196
15
27
-12
144
5
18
-13
169
10
22
-12
144
59
136
∑D = -77
∑D²= 999
M₁ = 9.83
M₂ = 22.6
Step 3 : Compute for the Mean
_
of the Difference Score (D) and
the Sum of Squares of Sample
Different Scores (SSD)
_ ΣD
-77
D=
= 6 = -12.83
N
(ΣD)²
SSD= ΣD²N
(-77)²
SSD= 999 - 6
SSD= 10.83
Step 4 : Compute for the t-statistics
_
D - μD
t=
SSD
√ N ( N-1)
t=
-12.83 - 0
√
10.83
6 - (6-1)
t = -3.9
D_ = difference score
D = mean of the sample
difference of the scores
μD = mean of the population
of the difference scores
N = number of the
difference scores
SSD = ∑ (D - D)² = sum of the
squares of sample
difference scores
Step 5 : Determine the Critical Value
df = N - 1
df = 6 - 1
df = 5
α = .05
Step 6 : Compare the t-statistics (computed value)
to the critical value from the table
t = -3.9
t - table = 2.571
If the value of t is greater than the value of table t,
reject the Ho.
Conclusion :
Example Problem :
6 Grade 12 student are selected to attend a lecture about Statistical Mathematics and given a
30 item test before and right after the said lecture.
Hypotheses:
Ho : There is no significant difference in the pre-test and post-test of Statistical
Mathematics scores
Ha : There is significant difference in the pre-test and post-test of Statistical
Mathematics scores
THANK
YOU!
Problem:
7 student of BSBA Financial Management students are chosen to join the spiritual retreat, then
answered religiosity measure before and after the religiosity retreat.
Pre-test
4
5
7
5
6
6
7
Pre-test
8
8
9
7
9
10
9
Hypotheses:
Ho : There is no significant difference in the pretest and post test of religiosity scores.
Ha : There is a significant difference in the pretest and post test of religiosity scores.