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Chapter 11Hypothesis Tests: Two
Related Samples
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Overview Learning objectives Vocabulary lesson again Introduce t test for related samples Advantages and disadvantages An example Review questions
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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
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Vocabulary Related-samples t statistic Repeated-
measures design Matched-samples design Difference scores (estimated standard error
of D-bar) Individual differences Carry-over effects
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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
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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
1,
ndfs
Dt
D
D
n
s
n
ssD
2
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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
Alternative states that
• There is a real difference0:
0:
1
0
D
D
H
H
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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
0:
0:
1
0
D
D
H
H
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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 PTSDBefore After Diff.
212421263227212518
1515172017208
1910
6946
157
1368
MeanSt. Dev.
23.844.20
15.674.24
8.173.60
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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
85.62.1
22.8
9
6.3022.8
n
sD
s
Dt
D
D
D
D
df = n - 1 = 9 - 1 = 8
Compute t test for related samples
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Step 4 The critical value with 8 df, α=.05, two-
tailed = +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.
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SPSS Next slide shows SPSS Printout
• Similar printout from other software
• Results match ours
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Magnitude of difference by computing effect size
Two methods for computing effect size
Cohen’s d
r2
s
DdsCohen _'
dft
tr
2
22
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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?
Cont.
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Review Questions--cont. Why 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?
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