1 Repeated-Measures Analysis of VarianceChapter 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 VarianceMajor Topics What are repeated-measures? An example Assumptions Advantages and disadvantages Review questions

3 Effects of Counseling For Post-Traumatic Stress DisorderChapter 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 VarianceTherapy 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 VarianceThe Data

7 Chapter 18 Repeated-Measures Analysis of VariancePlot of the Data

8 Preliminary ObservationsChapter 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 VariabilityChapter 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 VarianceCalculations Cont.

11 Chapter 18 Repeated-Measures Analysis of VarianceCalculations--cont.

12 Chapter 18 Repeated-Measures Analysis of VarianceSummary Table

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

15 Chapter 18 Repeated-Measures Analysis of VarianceAssumptions--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 VarianceMultiple 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 DesignsChapter 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 VarianceDisadvantages Carry-over effects Counter-balancing May tip off subjects

19 Chapter 18 Repeated-Measures Analysis of VarianceReview 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.