Mixed Model ANOVA
Adv. Experimental
Methods & Statistics
PSYC 4310 / COGS 6310
Michael J. Kalsher
Department of
Cognitive Science
PSYC 4310/6310
Advanced Experimental Methods and Statistics
© 2012 Michael Kalsher
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Outline
• Introduction to Mixed Model Designs
• Lab and practice data sets
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Sample Problem
An adult attachment researcher reads an article which
shows that insecure attachment can exert physiological
effects on children, including negatively impacting their
quality of sleep.
The researcher decides to investigate whether similar
effects may occur in married couples. Previous research
had indicated that periods of almost any kind of anxiety or
stress are also associated with sleep disturbances, such a
reduction in deep (delta) sleep. Stressed individuals exhibit
a tendency toward less and lighter sleep.
The researcher conducts a study to determine whether the
presence of a person’s spouse while sleeping reduces the
presence of sleep disturbances in individuals who are
stressed.
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Method
Participants. 30 women who had recently moved to a new area to
begin new jobs with their spouses. Among the women, 10 are secure,
10 are anxious, and 10 are avoidant in their attachment styles.
Procedure. The sleep patterns of the 30 women are monitored
while they sleep alone and while they sleep with their spouses. The
DV is the overall percentage of time spent in deep delta sleep.
Design. Two-way mixed ANOVA with one within-subjects factor and
one between-groups factor. Partner-proximity (sleep with spouse vs.
sleep alone) is the within-subjects factor; Attachment style is the
between-subjects factor.
H1: Subjects will experience significantly greater sleep disturbances in the
absence of their spouses due to the stressful nature of their present
circumstances.
H2: Subjects with secure attachment styles will derive comfort from the
presence of their spouses and will experience significantly more deep delta
sleep than subjects with insecure attachment styles.
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Data View
Attachment Style Key
1 = Secure
2 = Anxious
3 = Avoidant
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Variable View
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Step 1
Step 2
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Step 3
Step 4
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Step 5
Why add these two
factors? Why not
add “Partner”?
Step 6
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Homogeneity Assessment
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Main Analyses:
Repeated Measures
Note:
Partner “1” = Sleeping Partner Absent
Partner “2” = Sleeping Partner Present
Main effect of Partner
Partner x Attachment
Style Interaction
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Percent Time in Delta Sleep
Can you find the source of the interaction?
Partner Present
Partner Absent
Secure
Anxious
Avoidant
AttachStyle
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19.7
15.7
16.8
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Critical Values for F
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Mixed Model ANOVA:
Sample Problem
The statistics instructor at a local college is interested
in examining whether students’ scores on their stats
exams are influenced systematically by the time of
testing, the course instructor (there were three different
instructors), or whether the course is required (some
crazy students in other majors opt to take the course!).
Students took a pre-test at the beginning of the term, a
midterm and a final.
Which procedures will you use to analyze the data?
What is/are the Independent Variable(s)? Dependent
Variable?
What are the results?
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Subject
Pretest
Midterm
Final
Instruct
Required
1
56
64
69
1
0
2
79
91
89
1
0
3
68
77
81
1
0
4
59
69
71
1
1
5
64
77
75
1
1
6
74
88
86
1
1
7
73
85
86
1
1
8
47
64
69
2
0
9
78
98
100
2
0
10
61
77
85
2
0
11
68
86
93
2
1
12
64
77
87
2
1
13
53
67
76
2
1
14
71
85
95
2
1
15
61
79
97
3
0
16
57
77
89
3
0
17
49
65
83
3
0
18
71
93
100
3
1
19
61
83
94
3
1
20
58
75
92
3
1
21
58
74
92
3
1
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Mixed-Model ANOVA:
Variable View
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Mixed-Model ANOVA:
Data View
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Descriptive
Statistics:
what’s going on?
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Main Analyses: Repeated-measures
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Post-hoc Tests:
Decomposing the Main Effect of Time-of-Test
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Post-hoc Tests:
Decomposing the Instructor x Time-of-test Interaction
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Post-hoc Tests:
Decomposing the Instructor x Time-of-test Interaction
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Main Analysis: Between-Subjects Variables
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Writing up the Results
Mauchly’s test indicated that the sphericity assumption was violated for the
main effect of Time-of-test, 2(2)=14.96, p<.01. Therefore, degrees of
freedom were corrected using Huynh-Feldt estimates of sphericity (ε = .85).
There was a significant main effect of Time-of-testing, F(1.69,25.40)=868.21,
p<.01, partial eta-squared = .98. Test scores increased consecutively from
the pre-test (M=63.14, SE=2.04) to the Midterm (M=78.4, SE=2.38) to the
Final exam (M=85.96, SE=1.99). Post-hoc tests using the Bonferroni
procedure revealed significant differences between all three times of testing,
p’s<.01. The large effect size estimate suggests the observed increases in
test performance over time were substantial.
There was also a significant interaction effect between Time-of-testing and
Instructor, F(3.39,25.40)=62.37, p<.01, partial eta-squared = .89. As shown
in Figure 1, the difference in exam scores among the three instructors was
greater for the Final Exam than for either the Pretest or the Midterm.
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Figure 1. The difference in student test performance among the three instructors
was significantly greater for the Final exam than for the Pretest or Midterm.
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Sample Problem
An evolutionary view of jealousy suggests that men
and women have evolved distinctive types of
jealousy because male and female reproductive
success is threatened by different types of infidelity.
- A woman’s sexual infidelity deprives her mate of a
reproductive opportunity and in some cases burdens him with
years investing in a child that is not his.
- A man’s sexual infidelity does not burden his mate with
unrelated children, but may divert his resources from his
mate’s progeny This diversion of resources is signaled by
emotional attachment to another female.
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Jealousy Mechanisms: Men vs. Women
Men: Evolved to prevent his mate’s sexual infidelity.
Women: Evolved to prevent her mate’s emotional
infidelity.
Hypothesis - Men and women should divert their
attentional resources toward different cues to
infidelity, such that:
- Women should be on the lookout for emotional infidelity
- Men should be on the lookout for sexual infidelity
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Schutzwohl 2008 Study
Men and women saw sentences on a computer screen.
On each trial, participants saw a target sentence that was
emotionally neutral (“The gas station is at the other side of
the street”).
Before each of the neutral targets, a distractor sentence
was presented that was either affectively neutral or
indicated sexual infidelity.
If the distractor sentences grab a person’s attention then
they would remember them and they would not remember
the target sentence that follows. Further, these effects
should show up only in people currently in a relationship.
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IVs and DVs
IVs:
Relationship: The person has a partner or does not.
Type of Distractor: Neutral distractor vs. Emotional
Infidelity distractor vs. Sexual Infidelity distractor
Whether the sentence was a distractor or the target
following the distractor
DV:
Number of Sentences the person could remember.
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