SPSS Series 3: Repeated Measures ANOVA and MANOVA

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

2. 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 List of topics 2

3. 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? GLM Repeated Measures 3

4. 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. 4 GLM Repeated Measures

5. 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. 5 Repeated measures

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

7. 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 7 One-way within-subjects ANOVA

8. The design 8 One-way within-subjects ANOVA

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

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

11. 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 11 One-way within-subjects ANOVA

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

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

14. We don�t have any between-subjects factors Click Options to get this 14 One-way within-subjects ANOVA

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

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

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

18. 18 One-way within-subjects ANOVA

19. 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. 19 One-way within-subjects ANOVA

20. SPSS outputs The mathematical properties underlying the relationship between within-subjects factor and dependent variable. 20 One-way within-subjects ANOVA

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

22. 22 One-way within-subjects ANOVA

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

24. 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 ?2 = .003, which indicated no difference of frequency of drinking over time. 24 One-way within-subjects ANOVA

25. Two-way mixed design 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. 25 Two-way Mixed Design (ANOVA)

26. 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 26 Two-way Mixed Design (ANOVA)

27. The design 27 Two-way Mixed Design (ANOVA)

28. 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� 28 Two-way Mixed Design (ANOVA)

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

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

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

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

33. 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 ?2 = .003. 33 Two-way Mixed Design (ANOVA)

34. 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 34 Two-way Mixed Design (MANOVA)

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

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

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

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

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

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

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

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

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

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

45. 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, ?2 = .01. Univariate tests also indicated there was no intervention effect on individual drinking behavior, F(1, 285) = .90, p = .34, ?2 = .003 for frequency, F(1, 285) = .67, p = .41, ?2 = .002 for quantity, and F(1, 285) = .39, p = .53, ?2 = .001 for heavy drinking. 45 Two-way Mixed Design (MANOVA)

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

47. 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 47 GLM Repeated Measures Contrasts

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

49. 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. 49 GLM Repeated Measures Contrasts

50. SPSS outputs 50 GLM Repeated Measures Contrasts

51. 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. Reference 51

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