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Department of Cognitive Science

Adv. Experimental Methods & Statistics

PSYC 4310 / COGS 6310

Mixed Model ANOVA

Michael J. Kalsher

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 ProblemAn 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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MethodParticipants. 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

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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 effect of Partner

Partner x Attachment Style Interaction

Note:Partner “1” = Sleeping Partner AbsentPartner “2” = Sleeping Partner Present

Main Analyses: Repeated Measures

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Can you find the source of the interaction?

Secure Anxious Avoidant

AttachStyle

Partner Absent

Partner Present

Per

cen

t T

ime

in D

elta

Sle

ep

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19.7

15.716.8

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Critical Values for F

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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?

Mixed Model ANOVA: Sample Problem

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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 ResultsMauchly’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 ProblemAn 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.