1. SPSS Series 3: Repeated Measures ANOVA and MANOVA
By Hui Bian
Office for Faculty Excellence

2. List of topics Repeated measures ANOVA with SPSS
One-way within-subjects ANOVA with SPSS
One between and one within mixed design with SPSS
Repeated measures MANOVA with SPSS
How to interpret SPSS outputs
How to report results

3. GLM Repeated Measures
When the same measurement is made several times on each subject or case, such as
Same group of people are pretested and post-tested on a dependent variable.
Comparing the same subjects under several different treatments.
Interested in the performance trends over time: is it linear, quadratic, or cubic?

4. GLM Repeated Measures Between and within factors
Between factors: a grouping or classification variables such as sex, age, grade levels, treatment conditions etc.
Within factors: is the one with multiple measures from a group of people such as time.

5. Repeated measures Assumptions Independence of the observations
Violation is serious
Multivariate normality
Fairly robust against violation
Sphericity
Not necessary for the multivariate approach
The variance-covariance matrices are the same across the cells formed by the between-subjects effects.

6. One-way within-subjects ANOVA
A simplest design
One within-subjects factor
One dependent variable
A group of subjects measured at different points in time

7. One-way within-subjects ANOVA
Example: sample is from high school students.
Research questions:
1. whether there is a significant change on frequency of drinking over time (3 months) before and after treatment;
2. whether the relationship between the within factor (time) and frequency of drinking is linear, quadratic, or cubic.
Within-subjects factor: time.
Dependent variable: frequency of drinking (a28 and b28).
Two-time points data: a28 means baseline and b28 means 3-month posttest
Two conditions: before treatment and after treatment

8. One-way within-subjects ANOVA
The design
Conditions
Subjects
Before treatment
After treatment 1 2 3 4 . n

9. One-way within-subjects ANOVA
Select Intervention group as our sample
Go to Data Select Cases
Check If conditions…
Then click If

10. One-way within-subjects ANOVA
Let Conditions = 1
Then click Continue

11. One-way within-subjects ANOVA
Run Repeated Measures analysis
Analyze General Linear Model Repeated Measures
Type Time as Within-Subject Factor Name, type 2 as Number of Levels, then click Add
Type dv1 as Measure Name (dv means dependent variable), then click Add

12. One-way within-subjects ANOVA
Then click Define

13. One-way within-subjects ANOVA
After Define you should get this window
Move a28 to (1, dv1)
Move b28 to (2, dv2)

14. One-way within-subjects ANOVA
We don’t have any between-subjects factors
Click Options to get this
Check Compare main effects even we have two levels for within-subjects factor. I just want to show the pair comparison function.

15. One-way within-subjects ANOVA
Click Plots to get this window

16. One-way within-subjects ANOVA
SPSS outputs
Descriptive statistic results

17. One-way within-subjects ANOVA
SPSS outputs
Within-subjects effect: results of two tables are same.

18. One-way within-subjects ANOVA
Correction options include Geenhouse-Geisser, Huyn-Feldt, and Lower-bound when sphericity is not assumed. They produce more conservative estimates.

19. One-way within-subjects ANOVA
SPSS outputs
Within-subjects effect: if there is no homogeneity of dependent variable covariance matrix, the Sphericity is not assumed. We should use the correction options.

20. One-way within-subjects ANOVA
SPSS outputs
The mathematical properties underlying the relationship between within-subjects factor and dependent variable.
Test linear component of Time effect
The linear component is not significant

21. One-way within-subjects ANOVA
SPSS outputs
Plot

22. One-way within-subjects ANOVA
Quadratic
Cubic

23. One-way within-subjects ANOVA
SPSS outputs
Pairwise comparisons: the within-subjects factor only has two levels. So we get the same results as multivariate tests table shows.

24. One-way within-subjects ANOVA
Results
One-way within-subjects ANOVA was performed to test whether there was a difference of frequency of drinking between before-treatment and after-treatment conditions. The observed F value was not statistically significant, F(1, 136) = .42, p = .52, partial η2 = .003, which indicated no difference of frequency of drinking over time.

25. Two-way Mixed Design (ANOVA)
Two independent factors: one is a between-subjects factor and one is a within-subjects factor
One dependent variable.
Tests null hypotheses about the effects of both the between-subjects factor and within-subjects factor.
Tests the effect of interactions between factors.

26. Two-way Mixed Design (ANOVA)
Example:
Research questions:
whether there is a significant change on frequency of drinking over time (3 months) between intervention and control group.
Within-subjects factor: time.
Between-subjects factor: conditions (intervention vs. control).
Dependent variable: frequency of drinking (a28 and b28).
Two-time points data: a28 means baseline and b28 means 3-month posttest

27. Two-way Mixed Design (ANOVA)
The design
Conditions
Intervention
Control
Subjects
Time 1
Time 2 1 2 3 4 . n

28. Two-way Mixed Design (ANOVA)
Run repeated measures analysis
Select all cases
Go to Analyze General Linear Model Repeated Measures
The same procedure to define the within-subjects factor and dependent variable.
Move Conditions to…

29. Two-way Mixed Design (ANOVA)
Click Options
Click Plots

30. Two-way Mixed Design (ANOVA)
SPSS outputs
Multivariate tests

31. Two-way Mixed Design (ANOVA)
SPSS outputs
Estimated marginal means

32. Two-way Mixed Design (ANOVA)
SPSS outputs
Plots

33. Two-way Mixed Design (ANOVA)
Results
The intervention effect was analyzed using repeated measures ANOVA. There was no statically significant difference between intervention and control group over time on frequency of drinking, F(1,285) = .90, p = .34, partial η2 = .003.

34. Two-way Mixed Design (MANOVA)
Example
Research questions:
whether there is a significant change on drinking behaviors over time (3 months) between intervention and control groups; or whether there is an intervention effect on drinking behaviors.
Within-subjects factor: time.
Between-subjects factor: conditions (two levels)
Dependent variables: frequency of drinking (a28 and b28), quantity of drinking (a31 and b31), and heavy drinking (a34 and b34).
Two-time points data: baseline and posttest

35. Two-way Mixed Design (MANOVA)
Run repeated measures analysis
Go to Analyze General Linear Model Repeated Measures
We have three dependent variables
Still one within-subjects factor
Click Define

36. Two-way Mixed Design (MANOVA)
Move a28/b28, a31/b31, and a34/b34 to…

37. Two-way Mixed Design (MANOVA)
Options and Plots

38. Two-way Mixed Design (MANOVA)
SPSS outputs
Multivariate tests

39. Two-way Mixed Design (MANOVA)
SPSS outputs
Within-subjects effects

40. Two-way Mixed Design (MANOVA)
SPSS outputs
Univariate tests

41. Two-way Mixed Design (MANOVA)
SPSS outputs
Estimated marginal means

42. Two-way Mixed Design (MANOVA)
SPSS outputs
Plots: dv1 (frequency of drinking)

43. Two-way Mixed Design (MANOVA)
SPSS outputs
Plots: dv2 (quantity of drinking)

44. Two-way Mixed Design (MANOVA)
SPSS outputs
Plots: dv3 (heavy drinking)

45. Two-way Mixed Design (MANOVA)
Results
Repeated measures MANOVA test was conducted to test intervention effect on drinking behaviors. The results showed there was no difference between intervention and control group on frequency, quantity, and heavy drinking over time, F(3, 283) = 1.18, p = .32, η2 = Univariate tests also indicated there was no intervention effect on individual drinking behavior, F(1, 285) = .90, p = .34, η2 = .003 for frequency, F(1, 285) = .67, p = .41, η2 = for quantity, and F(1, 285) = .39, p = .53, η2 = .001 for heavy drinking.

46. GLM Repeated Measures Contrasts
Example (planned comparisons)
One within-subjects factor: time
One between-subjects factor: living condition (11r)
One dependent variable: frequency of drinking (a28 and b28)

47. GLM Repeated Measures Contrasts
Contrasts are used to test for differences among the levels of a between-subjects factor.
Go to Analyze General Linear Model Repeated Measures
The same procedure to define within-subjects factor and dependent variable
Click Contrasts

48. GLM Repeated Measures Contrasts
You should get the left window
Choose Simple (simple means compares the mean of each level to the mean of a reference).
Pull down

49. GLM Repeated Measures Contrasts
Decide which category of between-subjects factor is a reference category.
The between-subjects factor is a11r: 1= Mother and father; 2 = Mother and stepfather; 3 = Mother; 4 = Others.
Use 1 = Mother and father as a reference.
Check First, then click Change

50. GLM Repeated Measures Contrasts
SPSS outputs

51. Reference
Meyers, L. S., Gamst, G., & Guarino, A. J. (2006). Applied multivariate research: design and interpretation. Thousand Oaks, CA: Sage Publications, Inc. Stevens, J. P. (2002). Applied multivariate statistics for the social sciences. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.

52. Thank you