1 of 29 advanced experimental methods and statistics mixed model anova michael j. kalsher © 2014...

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Advanced Experimental Methods and

Statistics

Mixed Model ANOVA

Michael J. Kalsher

© 2014 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 Greenhouse-Geisser estimates of sphericity (ε = .60).

There was a significant main effect of Time-of-testing, F(1.20,18.11)=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.