1. Repeated-Measures Analysis of Variance
Chapter 18
Repeated-Measures Analysis of Variance
Fundamental Statistics for the Behavioral Sciences, 4th edition
David C. Howell
©1999 Brooks/Cole Publishing Company/ITP   

2. Chapter 18 Repeated-Measures Analysis of Variance
Major Topics
What are repeated-measures?
An example
Assumptions
Advantages and disadvantages
Review questions

3. Effects of Counseling For Post-Traumatic Stress Disorder
Chapter 18 Repeated-Measures Analysis of Variance
Effects of Counseling For Post-Traumatic Stress Disorder
Foa, et al. (1991)
Provided supportive counseling (and other therapies) to victims of rape
Do number of symptoms change with time?
Point out lack of control group
Not a test of effectiveness of supportive counseling
Foa actually had controls.
Foa, E.B., Rothbaum, B.O., Riggs, D.S., & Murdock, T.B. (1991). Treatment of posttraumatic stress disorder in rape victims: A comparison between cognitive-behavioral procedures and counseling. Journal of Consulting and Clinical Psychology, 59,
Cont.

4. Effect of Counseling--cont.
Chapter 18 Repeated-Measures Analysis of Variance
Effect of Counseling--cont.
9 subjects measured before therapy, after therapy, and 3 months later
We are ignoring Foa’s other treatment conditions.

5. Chapter 18 Repeated-Measures Analysis of Variance
Therapy for PTSD
Dependent variable = number of reported symptoms.
Question--Do number of symptoms decrease over therapy and remain low?
Data on next slide

6. Chapter 18 Repeated-Measures Analysis of Variance
The Data

7. Chapter 18 Repeated-Measures Analysis of Variance
Plot of the Data

8. Preliminary Observations
Chapter 18 Repeated-Measures Analysis of Variance
Preliminary Observations
Notice that subjects differ from each other.
Between-subjects variability
Notice that means decrease over time
Faster at first, and then slower
Within-subjects variability

9. Partitioning Variability
Chapter 18 Repeated-Measures Analysis of Variance
Partitioning Variability
Total Variability
Between-subj. variability
Within-subj. variability
Time
Error
This partitioning is reflected in the summary table.

10. Chapter 18 Repeated-Measures Analysis of Variance
Calculations
Cont.

11. Chapter 18 Repeated-Measures Analysis of Variance
Calculations--cont.

12. Chapter 18 Repeated-Measures Analysis of Variance
Summary Table

13. Chapter 18 Repeated-Measures Analysis of Variance
Interpretation
Note parallel with diagram
Note subject differences not in error term
Note MSerror is denominator for F on Time
Note SStime measures what we are interested in studying

14. Chapter 18 Repeated-Measures Analysis of Variance
Assumptions
Correlations between trials are all equal
Actually more than necessary, but close
Matrix shown below
Cont.

15. Chapter 18 Repeated-Measures Analysis of Variance
Assumptions--cont.
Previous matrix might look like we violated assumptions
Only 9 subjects
Minor violations are not too serious.
Greenhouse and Geisser (1959) correction
Adjusts degrees of freedom

16. Chapter 18 Repeated-Measures Analysis of Variance
Multiple Comparisons
With few means:
t test with Bonferroni corrections
Limit to important comparisons
With more means:
Require specialized techniques
Trend analysis

17. Advantages of Repeated-Measures Designs
Chapter 18 Repeated-Measures Analysis of Variance
Advantages of Repeated-Measures Designs
Eliminate subject differences from error term
Greater power
Fewer subjects needed
Often only way to address the problem
This example illustrates that case.

18. Chapter 18 Repeated-Measures Analysis of Variance
Disadvantages
Carry-over effects
Counter-balancing
May tip off subjects

19. Chapter 18 Repeated-Measures Analysis of Variance
Review Questions
What makes a repeated-measures design different from a between-subjects design?
What happens to the error that is lost from the error term?
Why don’t we test for differences between subjects?
What assumptions are required?
Cont.

20. Review Questions--cont.
Chapter 18 Repeated-Measures Analysis of Variance
Review Questions--cont.
What does the Greenhouse and Geisser correction do?
Why do we limit the number of t tests we would run between means?
What are the advantages and disadvantages of repeated-measures analysis of variance?
Cont.

21. Review Questions--cont.
Chapter 18 Repeated-Measures Analysis of Variance
Review Questions--cont.
Describe a study where repeated- measures would be profitable.
Describe a study where repeated- measures would be a mistake.