Chapter 11
Hypothesis Tests: Two
Related Samples
Overview
 Learning
objectives
 Vocabulary lesson again
 Introduce t test for related samples
 Advantages and disadvantages
 An example
 Review questions
2
Learning Objectives
 Difference
between independent-measures
& related-samples experimental design
 Difference between repeated-measures &
matched-subjects experimental design
 Compute t test for dependent groups
 Advantages and disadvantages
 Measures of effect size
3
Vocabulary
 Related-samples
t statistic Repeated-
measures design
 Matched-samples design
 Difference scores (estimated standard error
of D-bar)
 Individual differences
 Carry-over effects
4
Related-samples t statistic
 Two
forms
• Repeated-measures design
• Matched-samples design
 Use difference scores between two
measurement points rather than means
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Repeated-measures
 The
same participants give us data on two
measures (e. g. Before and After treatment)
• Aggressive responses before video and
aggressive responses after
 Accounts for the fact that if someone is high
on one measure probably high on other.
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Matched-samples
 Individuals
in one group are matched to
individuals in a second sample
• Matching based on variables thought to
be relevant to the study
• Not always perfect match
 Also called matched pairs or pairwise t test
7
Difference Scores
 Calculate
difference between first and
second score (between individual scores or
matched pairs)
• e. g. Difference = Before – After
• D = X2-X1
 Base subsequent analysis on difference
scores
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The Formulas
D  D
t
, df  n  1
sD
sD 
2
s
s

n
n
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Hypothesis Testing
 Null
states that
• The population of difference scores has a
mean of zero
• No systematic or consistent difference
between the conditions
H 0 : D  0
 Alternative states that
H1 :  D  0
• There is a real difference
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Advantages of Related Samples
 Eliminate
subject-to-subject variability
• Makes the test more powerful
 Control for extraneous variables
 Need fewer subjects
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Disadvantages of Related
Samples
 Order
effects
 Carry-over effects
 Subjects no longer naïve
 Change may just be a function of time
 Sometimes not logically possible
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An Example
 Therapy
for rape victims
• Foa, Rothbaum, Riggs, & Murdock
(1991)
 A group (n=9) received Supportive
Counseling
 Measured post-traumatic stress disorder
symptoms before and after therapy
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Step 1
 Null:
there is no difference in symptoms in
individuals after treatment
 Alternative: there is a difference in
symptoms
 α=.05, two tailed
H 0 : D  0
H1 :  D  0
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Step 2
 With
a sample of 9
• df = n-1 = 9-1 = 8
• Critical value = +2.306
 Sketch
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The Data: Therapy for PTSD
Before
Mean
St. Dev.
21
24
21
26
32
27
21
25
18
23.84
4.20
After
15
15
17
20
17
20
8
19
10
15.67
4.24
Diff.
6
9
4
6
15
7
13
6
8
8.17
3.60
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Eye test of Results
 The
Supportive Counseling group
decreased number of symptoms
 Was this enough of a change to be
significant?
 Before and After scores are not
independent; use related-samples t test
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Step 3
Compute t test for related samples
D   D D   D 8.22  0 8.22
t



 6.85
sD
3.6
1.2
sD
n
9
df = n - 1 = 9 - 1 = 8
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Step 4
critical value with 8 df, α=.05, twotailed = +2.306
 We calculated t = 6.85
 Since 6.85 > 2.306, reject H0
 Conclude that the mean number of
symptoms after therapy was less than mean
number before therapy.
 Supportive counseling seems to work.
 The
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SPSS
 Next
slide shows SPSS Printout
• Similar printout from other software
• Results match ours
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Paired Samples Statistics
Mean
Pair
1
Std.
Deviation
N
Std. Error
Mean
POST
15.6667
9
4.2426
1.4142
PRE
23.8889
9
4.1966
1.3989
Paired Samples Correlations
N
Pair 1
POST & PRE
Correlation
9
.637
Sig.
.065
Paired Samples Test
Paired Differences
Mean
POST - PRE
-8.2222
Std.
Deviation
Std. Error
Mean
3.5978
1.1993
95% Confidence
Interval of the
Difference
Lower
Upper
t
-10.99
-5.46
-6.86
df
Sig.
(2-tailed)
8
.000
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Magnitude of difference by
computing effect size
 Two
methods for
computing effect size
 Cohen’s
 r2
d
D
Cohen' s _ d 
s
2
t
r2  2
t  df
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Review Questions
 Why
do we say that the two sets of measures
are not independent?
 What are other names for “related samples?”
 How do we calculate difference scores?
• What happens if we subtract before from
after instead of after from before?
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Cont.
Review Questions--cont.
do we usually test H0: D = 0?
 Why do we have 8 df in our sample when
we actually have 18 observations?
 What are the advantages and disadvantages
of related samples?
 Why
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