The document provides information about conducting a dependent t-test, also known as a paired samples t-test. It is used to compare two dependent or related samples, such as the same group measured at two different time points. The test involves calculating a t-statistic based on the mean difference between pairs and comparing it to a critical value from a t-distribution to determine if the difference is statistically significant. Examples are given of research questions and study designs that could use a dependent t-test to analyze data. The steps of the test procedure are outlined, including stating hypotheses, setting an alpha level, calculating the t-statistic, comparing it to critical values, and making a decision about the null hypothesis.

1. Week 9:Dependent t-test
Paired Samples t- test for two dependent
samples
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2. Dependent Samples
 When have two dependent or related
samples.
• Same group measured twice (Time 1 vs. Time
2; Pretest and Posttest).
• Samples are matched on some variable.
 Each score in one sample is paired with a
specific score in the other sample.
 Such data are correlated data.
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3. Examples of Research
Questions:
 Is there a significant difference students’
mathematics achievement when taught
through traditional methods and hands-on
problem-solving method?
IV = method taught (values = traditional
[baseline], hands-on problem-solving)
DV = mathematics achievement (score,
continuous)
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4. Examples of Research
Questions:
 Is there a significant difference in
morbidly obese students’ pre-exercise
weight and post-exercise weight?
 Rather than comparing the means of the
pre and post, we compare the pre and post
scores for each individual.
IV: Time (pre or post)
DV: Weight (Value = pounds, continuous)
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5.  An investigator for NASA examines the effect of cabin
temperature on reaction time. A random sample of
10 astronauts and pilots is selected. Each person’s
reaction time to an emergency light is measured in a
simulator where the cabin temperature is maintained
at 70 degrees F and again the next day at 95
degrees F.
IV: Temperature (values = 70F or 95F)
DV: Reaction Time (Value = seconds, continuous)
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6.  Is there a significant difference between
husband and wife’s annual income?
IV: Spouse (values = husband, wife)
DV: Annual income (Value = dollars, continuous)
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7. Steps in hypothesis testing:
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8. Step 1:State the hypotheses
Null hypothesis:
H 0:µ D = 0 or Ho: µD ≥ 0 or Ho: µD ≤ 0
Alternative hypothesis:
H 1:µ D
≠0
or H 1:µ D
>0
or H 1:µ D
<0
* Subscript D indicates difference.
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9. Step 2: Set Criterion for
Rejecting HO
1) Compute degrees of freedom
df = n – 1 whereby n = number of pairs
2) Set alpha level
3) Locate critical value(s)
 Table C. 3 (page 638 of text) – same as
in an Independent t - test
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10. Step 3: Compute test statistic
Whereby:
D = x2 − x1 D
after-before
Sum of
individual t=
D =
∑D
n
differences
S D
S = Sample Standard Deviation S D
D
of difference (D) scores, divided
by n
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11. D
t=
Example Computation: S D
∑ D = 1+1+1+ 3 + 0 + 2 = 8 Before After D = after - before
D=
∑ D = 8 = 1.3 Standard
5
8
6
9
1
1
n 6 deviation of the 4 5 1
differences
=S
1.03 3 6 3
S D
D
n
=
6
= .42 7 7 0
Number of 8 10 2
pairs
D 1 .3
t= = = 3.09
S D
.42
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12. Step 4: Compare Test Statistic to
Criterion
 Use t distribution in the
appendix to find the critical
values (given alpha level, df,
and directionality of the test).
 In this example,
df = n-1= 6-1 = 5
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13. Step 5: Make decision
 Use t distribution in the appendix
to find the critical values (given
alpha level, df, and directionality
of the test).
 The graph on the right shows an
example of two-tailed test with
the c.v. equal to ± 2.776.
 For our example, use Table C.3 on
page 638 to find out the critical
value(s). With alpha = 0.05 and
df = 5, the critical values are ±
2.571 (two-tailed test).
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